How do I get to bosses relatively intact?

etrian-odyssey-4

There's a lot of various tricks to take into mind when figuring out how to get to bosses intact. You've basically got 4 resources to manage, which in order of priority, are TP, HP, Items, Burst Gauge. Of these, the last I won't even really talk about - Burst Gauge is convenient but builds up a lot easier during battle so it's not nearly as important to "Top off everyone before the fight!" as the Boost/Force/Limit gauges of the previous games. Items are easy to preserve by just by not using them - they're not as much a priority as TP but because there are no means to nullify or reverse item costs like with TP, it's nicer to avoid using. There are some points, though, so there are a few bullet points there.

I will first give some generic strategies to start off, then I'll go further into maze-specific strategies (for now, only up to the 4th maze). As a note, there are bullet points for each of the hidden classes so these are prefaced accordingly if one wants to skip those points.

Some General Advice

You already know about the importance of shortcuts, but I'll repeat it here all the same. Most mazes have a lot of shortcuts which should cut down encounters significantly on the trip down.
Additionally, most mazes may have one or more spots to recover resources along the way, either party-wide or to a single member. If you know where these are you can scope your spending around them to basically have that much extra TP/HP. If you decide to play with time, these always reset at midnight so you can time it so that you arrive just before midnight and get twice the healing.
It goes without saying that fewer battles means less costs incurred. Consider investing in Warding Bells when you unlock them in the store (though you get a fair number of them from quests for the first few mazes before then). A Sniper with Camouflage offers more effectiveness and longer duration at the cost of TP, but one person's small TP spending can be worth a whole lot from the rest of the party's not-spending.
As asserted at the top, Burst Gauge can replenish itself pretty easily, since it essentially costs nothing to refill. There are some encounters that can be pretty nasty... unless you just eliminate most of the threat with say a well-placed Flame Wall or Double Slash. Calm Breath is also an excellent healing tool at only one gauge for a ~50% HP heal. Swipe Slash is costly at 4 gauges but an all-enemy kill is absolutely hilarious to see.
TP is worth more than HP, since there are mounds of ways to passively heal HP (and of course a slew of healing skills for TP) but few to recover TP. A single Amrita's 30 TP, well used, can be worth the equivalent of several HP healing items in your pack. Consider this when planning your items during the journey. Of course, during the boss fight using HP healing can be helpful, so it's more like, consider having an Amrita or two for the walk.
You have a whopping 60 item slots. On a trip to fight a boss, you want to fight as few enemies as possible, which means you shouldn't be getting a lot of enemy drops. So don't be afraid to stock up a bit more than normal for the boss run, both for the boss itself but also for the trek if necessary. Items aren't wasted if they let you win in the end. Keep in mind the above bullet point.
If one or more characters do not already have them in your planned equipment for the boss fight, consider equipping some TP-boosting items for the journey in place of pure defense items and such. This gives you a good pool of TP to basically use for free. Items that have TP icons like the Brilliance Belt scale off of your TP so are best for classes with high TP, while flat TP boosts like from the Dragon items that Wiglaf can give will be useful to lower TP classes. Then when you are at the boss's door you can switch to their normal equipment. This can also be done with HP boosting items but TP is worth more to spend and HP is easy to recover, so generally not worth it comparatively. Again, you have 60 item slots, equipment is a fancy use for them.
In a similar vein, you may also consider extra Shoes and/or AGI-boosting equipment for the journey. Being able to act before the enemy can be exceptionally handy for some classes it will save you a lot of grief.
Determine what the most problematic encounters are and the easiest methods to get past them for minimal cost. For example, in the 2nd Maze, Black Claws can be nasty with an AoE slash attack that causes nasty poison damage. However, the TP cost for an arm bind is probably a lot less than the costs you'll spend trying to recover all that damage. I'll give some quick notes in the maze-specific strategies but in general, be aware of what packs of enemies you run into and try to see what counters them easiest.
Building off of that, passive recovery skills are exceptionally helpful. A Medic's Patch Up isn't a huge amount but if you can work with keeping your damage under it or roughly sane to it, that's still a good position. A Veteran Fortress can have Healing Wall to also provide some admittedly small healing to their row.
One point in a Medic or Runemaster's TP Boost is worth a whole 10% TP. If you have a spare point it may be handy.
Speaking of skill points... A skill usually sees a TP cost increase (and an accompanyingly larger effectiveness boost) at half-max and at max. While the effectiveness boost is very handy, if you don't need it on the normal enemies, you can consider just keeping skill points spare to top them off when you're about to face the boss. No need to spend extra TP when you don't need to.
Look at TP saving abilities. At the start you only have a Fortress's proficiency line (3/4/5 TP per facehit when in the front line) and a Runemaster's Free Energy, but these both can be useful to reduce the amount of TP you spend. Later on, you'll access the hidden classes, all of which have at least one means of TP recovery, so mix in some creative subclassing and you can start seeing some degree of being able to use low-cost abilities during normal fights for minimal or no TP cost.
If you find yourself in a battle that you can eliminate all but one mostly-harmless enemy, you can use this time with certain class combinations to work off active or passive recovery during battle. Defending with everyone but the one person who needs to use actions to restore HP and/or TP can make some good distance if this is setup to your favor.

Classes

I'm going to focus purely on "preservation". For some classes this basically boils down to their killing ability which I will only sparsely cover as that has a lot of approaches that boil down a lot to your own style. Just a heads up.

Landsknechts basically kill things, and they are more than capable of doing this without needing to use TP thanks to Initiative and Power Boost. They also have Swordbreaker which is as helpful in normal fights as it is against bosses. As active skills go, all they bring to the table is Bandage, which cheap as it is can prove prohibitively expensive for their low TP pools unless you have an appropriate subclass.

As a subclass, the main offering for preservation is Bandage to higher TP characters (or someone like a Fortress who recovers TP). I skimped much on talking since the base class Landsknecht has low TP, but Bandage does offer fairly decent recovery regardless of stats for its cost. It is also amplified by an ally Medic, so it is not in fact conflicting to have it in spite of a Medic on the same party.
Nightseekers are an interesting bunch. They have a decent amount of TP, and in terms of disables, theirs are fairly cheap. Sand Throw is a mere 3 TP even at max and Blind can be exceedingly handy in random battles, so even without a means of TP recovery/reduction, they can reliable throw that out. Venom Throw costs more but it has very high poison damage for its cost. Auto Spread makes it even nicer as a battle start effect. Do keep in mind though that when you step out of the status skills and into their major damage skills, the TP costs jump sharply so you have to still be somewhat reserving of them for when it's necessary.

Sneak Attack is an appreciable alternative to the Sniper's Camouflage, as battles are still usually inevitable so getting that first free turn can be a game-changer. Past this, Nightseekers are like Landsknechts and are thus fairly capable of killing well without any TP use past initial status hits.
Fortresses offer a unique form of a preservation due to lack of self-preservation. In seriosity, between Taunt and Auto-Taunt, and actively using their various shield skills, they can redirect most if not all damage to themselves. Which they can also reduce or nullify as needed. As their proficiency line recovers TP with each hit they take, it's self replenishing too. To a point, armed with the Calm Breath Burst Skill, a Fortress could basically keep the entire party in top shape without any other class contributing active or passive healing such as from a Medic.
Snipers deal with binds. Snipers don't have a wealth of TP without an appropriate subclass but their shots are still cheap, so as an earlier bullet point mentioned, don't be stingy if that one binding shot is all you need to save everyone. They also have the Camouflage skill as mentioned earlier. Solid all around basically. I'd give more notes about binds but because a Sniper is a targeted shot, there's little reason to not use the bind best suited for the target.
Medics are often a hard choice for many. They have a good TP pool but no recovery and reduction, and their healing spells and passives are useful for both the journey and the boss. Each heal during the journey is one less heal during the boss. They do have Patch Up, though, and you can use TP boosting equipment as with the Runemaster to have free healing. Actually what one of the best things they bring is their proficiency line, as it improves everyone's healing skills. Handy with, for example, someone with Bandage. At the end they aren't slouches if put in the front row with a hammer or subclass weapon, so they rely on passives (including Auto-Heal and Auto-Revive) to keep people up and running alongside Patch-Up.
Runemasters don't do much without spending TP, but given that they have Free Energy to null costs occasionally, combined with a massive TP pool and TP Boost, that isn't actually much of a problem. Equip TP boosting equipment for the travel and rely on the basic Runes and you'll be able to punch through random battles a lot easier on your mind. This becomes much more usable as you get further into later dungeons. Of note, Lightning Rune has the highest attack power of the basic runes and hits full damage across a whole row, so outside of encounters where enemies resist it, it can be fairly reliable if your setup is not geared towards weakness-striking.
Dancers are in an odd position because their active skills are primarily geared at prolonged engagements. When trying to dash to a boss, you don't particularly want prolonged engagement. Though I will point out that Energy Tango may be costly for the Dancer but its cost reduction to allies can be exceedingly handy. They are an attacking class though so while they don't have the raw power of others they still can do great without using TP before the boss.

Passives, though, the dancer has many useful ones to offer as both a main and a sub. Fan Dance and Speed Boost improve your ability to take down foes without damage. Burst Saver can allow you a bit more freedom in using Burst Skills during the journey. It's not necessarily reliable but Mist Dance also can save you if you don't want to use the more solid effects of Blind or a Bind.
Arcanists are the first hidden class, and they offer incredible help in preservation, not just for the individual but for the party as a whole. Their wide-area binds and statuses, especially with speed to act first, can nullify the danger of entire crowds of enemies at once. This is the most important thing they bring and it can't be ignored. Note that if enemies comprise multiple types to which one bind won't stop all skills, remember that Arm Bind sharply reduces physical attack while Head Bind sharply reduces non-physical attack (though there are few such skills that are not themselves head skills). Combined with Circle Boon to heal during battle while a circle is up, and Healing Steps to heal each step in the dungeon, that's a lot of passive healing. Then it all tops off with TP Return as well as the proficiency line that recover TP when a status or bind hits, and when a circle goes away or is dismissed. It's a bit overkill because they have fairly high TP pools to begin with and on a boss you probably won't touch most of it because of this. So they don't need to be as withholding as the Runemaster or Medic.

Even if you don't bring a main class Arcanist, it can be handy as a subclass. Healing Steps works with anyone, and TP Return can allow a Sniper or Nightseeker to smash enemies for good damage either for no cost or for minimal cost. If you don't outright use the circles anyway, that is.
Bushi are the second hidden class, and they offer incredible self-preservation in the form of their Deep Breath, which recovers not only a decent amount of HP but also a huge chunk of TP (20/30/40/50 for each level respectively). It has high priority, right after Burst Skills, so pairing it with Auto Surge basically means that the occasional battle is free TP recovery on folks while the rest of the party sweeps. This alone has made them exceptionally popular as a subclass, on top what else they offer for direct combat.

As a main class, Bushi aren't a slouch either, though they have low TP. Aside from Deep Breath, their proficiency line recovers TP purely by using normal attacks, so you can often use some skills to clear threats in the first turns of random fights, and recover with regular attacks for the rest of the fight. They also get Ferocity which heals HP with regular attacks, making it pretty well rounded (and often offsetting the damage from Blood Surge).
Imperial is the last hidden class, and it offers a certainly unique approach to survival. Their Drive skills may cost a chunk but since it can often eliminate a whole threat at once, that can be quite worth it. Impulse Edge is a strong TP recovery option that can easily offset that cost, whether you do it in the battle or even at the boss. In fact as long as Impulse Edge can be reliably landed, TP isn't much an issue for Imperials. Opposer and Finisher also give passive TP recovery for hitting weaknesses and killing, useful as both a main and a sub.

Maze Specific Advice

Eventually I'll add some actual coordinate data when I have my 3DS on me. I'll only cover mazes I've actually reached, but thus far we have...

Lush Woodlands

There are actually no relevant shortcuts on B1F, but on B2F there's a fair number that goes pretty much straight across the map to the Bloodbear's room. Enemies here aren't much of a threat, though. Jig Lizards can still be hit when camouflaged if they are Leg Bound or Blind if you want some quick advice. Deathstalkers are largely not worth the trouble to fight but Ice Coffin burst skill will make short work of them.
There's two major recovery spots. In B2F, just a ways off the shortcut path, you can pick fruit for 10 TP to the entire party. In B3F, a bit ways off, there's a resting spot that is either a guaranteed 5 TP to the party, or it could be 25 TP to the party with a risk of a Jig Lizard ambush instead. The fruit is pretty reliable so if you run into things on the first two floors, remember that everyone can basically have 10 more TP to spend (or 20 if you time midnight).
The boss fight does not begin the moment you step into the boss room. You in fact can eventually map out a shortcut that ends up right behind the boss from right near the stairs to B2F. As such, if you can't make it to the boss on your initial run through the boss door, this extra shortcut will make the journey even smoother.

Misty Ravine

There are small shortcuts in all three floors, but you still have quite a lot of walking to do. Consider a Warding Bell just to make the journey a bit more bearable.
Black Claws, as mentioned earlier, can be stopped easily with Arm Bind. Most other things, such as Raging Boars and Great Lynxes, a Fortress is pretty handy to take focus fire. A well placed Flame Wall can often eliminate the lines of Hollow Roamers you might find on B3F. Head Bind can prevent a Fire Bulb from exploding on you if you aren't fast enough to kill it early.
Travel during the day time is actually a generally nicer plan, as Black Claws only show up during the night.
There is one recovery spot in B2F, a small bit north of the shortcut path to B3F. It offers 40 HP and 10 TP to one member, which isn't a whole lot but it is something if you need it.
Big advantage here is having Wufan. She has Healing Steps and Circle Boon from the get-go, and can easily land binds across the enemy lines for easy fights (of which Leg Bind is also handy for the Hollows to negate their evasion). You may consider waiting for circles to expire for her proficiency skills to recover her TP for even more sustenance (net loss of 2 from her 10 cost circles if you expire it naturally, net loss of 6 if you use Dismiss Blow for an earlier end). She's a great introduction to how Arcanists can help make the journey smoother, and in this point she doesn't even take a party slot.

Golden Lair

There is a set of shortcuts from the Geomagnetic Pole that basically drop you down to B3F without any chance of enemy encounters. Ice Stakes aren't wholly necessary on the way down as there are a few right-along-the-way spots on B3F, though the nearest spot in B1F wouldn't hurt for two extra.
Magma Spawns and Glacier Spawns are much less nasty if Head Bound, if you don't have a Runemaster to just eliminate them with spells/Burst skills. Baboons should be Arm Bound to reduce their threat potency.Jumping Frogs and Zapper Frogs won't do as much if they are Leg Bound. There's a lot of different threats but thankfully they're usually all the same bind type.
There are two recovery spots, one a great deal away on B1F and one barely off the shortcut path in B2F. You'll need an Ice Stake for each, but it's worth 20 TP to one member each. That's pretty nice... except that the shortcut path is so incredibly short for B1F and B2F that unless you didn't sleep the night before there is little reason to need these. But if you need them, they are there.
Ice Spikes are in no short supply and are worth a small amount of Ice damage. While it ain't humongous, it will often beat the damage of normal attacks of certain classes (Arcanist and Runemaster) without costing any TP and also being notably effective on Magma Cores that you find en masse in B3F. Just be sure to keep some handy.
An Arcanist is extremely handy here. Nevermind that Tame Ground and Healing Steps are handy for those accursed scales, but a lot of the most dangerous encounters on B3F are in crowds that all are vulnerable to the same bind type as mentioned earlier. In other dungeons an Arcanist will be a convenience, but here they vastly change the journey for the better.
Kibagami is a Bushi/Medic, which means he can use healing spells fancy enough while also recovering his own TP with ease. He is a great bit off the beaten path to pick up, but since he's a sixth member and can offer this healing, don't skip him. In later trips to refight the boss, you won't need the lengthy detour.
Like in the Lush Woodlands, the boss here doesn't fight the moment you enter the room. There's a side room from the boss chamber that contains a Chop spot for 5 Ice Stakes, and more relevantly cuts travel time significantly and avoids all of the scales outside. So if you take too much pain from monsters on the way to the boss, consider just opening this shortcut and then coming back revitalized. Do consider the same time manipulation trick to get more Ice Stakes.

Echoing Library

The shortcuts in the central areas of each floor will allow for an exceedingly short trip to reach the boss chamber. The longest trek will be on B1F and even that won't be too long (and is one of few that is shorter from airship than from Geomagnetic Pole). B2F and B3F are almost entirely bypassed with their shortcuts.
Arm Bind will probably be the most universally useful just for the damage reduction, though it also stops the nasty attacks of Medusa Trees, Flame Lynxes, Proto-Bots, and Blue Wallabies. You'll want Leg Bind for Peach Crows, and as with their predecessors Purple Anoirs can still be hit if you Blind or Leg Bind them (and often with Paralyze, too). Cursed Shrooms will not explode if you kill them while they are Head Bound, but be mindful that curse backlash won't hit you if you actually kill the enemy with the attack.
There is one recovery spot worth a whopping 150 HP and 40 TP to the whole party. However, it's a bit off the beaten path on B1F, and always ends with an encounter against two Peach Birds separated by row. Without a Bushi in your team, there is a chance you could be attacked without the recovery. Still, if you find it handy from a bad encounter on the initial walk, it's not a space to be forgotten.
If, by some miracle, you did not have Logre's attack power demonstrated on your face firsthand, you should know that Logre can basically erase many enemies in a single hit. He can also recover his TP with Impulse Edge. All in all, don't be afraid to use his abilities to eliminate problem enemies with ease during your trek on B3F. Though if you unlocked all the shortcuts it'll be criminally short. Of note, though, his accuracy isn't the best so consider some means to assist his hitting.