Are the summoned Eidolons useful in any battles?
I only (usefully) summoned one Eidolon in my entire playthrough, and that was only because I did not have Renew at the time, so it was the easiest way to cure all of my characters.
When I obtained the first couple of Eidolons, I tried them out in a few battles, but they just did not do enough damage to justify the 3 TP required to summon them. Often it seemed like just letting your characters stagger and raise the chain gauge was a better option in each battle.
Are there any Eidolons that are useful, at any point in time? Are there specific enemies that are easier to defeat with a summoned Eidolon?
The main strength to Eidolons is raising the chain gauge while being able to avoid damage and ressurect your party (When Eidolons leave you are left with full health even on previously KO'd members).
As identitycrisisuk said, If you summon an Eidolon during a fight with an Adamantoise, It will cause the legs to die, which makes it fall on its face. During this phase it cannot attack, due to the difficulty of these monsters as well as the great CP they give (40K) and chance to drop Platinum Ingots (Sells for a ton) and Trapzohedron (Used for Crafting). It has become a very popular practice to start the battle off with a summon to make it much easier (Certain strategies are used to kill it before it gets back up). So this is one such enemy that answers your question.
I had trouble with a few random encounters through out the game and found that waiting until i was about to die, then summoning an eidolon was just the right move that needed to be done to stagger the tough enemies and eventually lead me to victory. TP is very easy to get in this game so i don't really consider this a waste.
Also, Bahamut is most likely the first way you will be breaking damage limit early in the game, and Hecatoncheir (Vanille's Summon /spelling) is good for inflicting status effects while you can buff yourself or spam death.
It should also be noted that everytime you get a Crystarium Upgrade, Your summons get stronger (Maxing out at the last Crystarium Upgrade, after the final boss).
The only use I know of is to take down the giant-tortoise type creatures - I haven't beaten any others than the one's you have to during the story though. The advantage here is that you can call in your summon right at the start and it should take out their front legs much quicker than if you tried to do it with normal attacks. This means you can avoid their stomp attacks that might otherwise kill your entire party right at the start of the battle and if you have TP restoring items you can call in a summon again if it manages to stand up again. I think there are better non summon ways of beating the tortoises but I didn't really get into it that deeply and it helped me out enough.
They are useful in 2 ways in general that I have not seen listed here already.
- You are guaranteed to be alive during the time one is summoned, and after be at full health. Thus, if an enemy has a huge attack, you can be spared the brunt of it by a summons.
- They are useful for killing small enemies, especially when there is a ton of them. There aren't a whole lot of battles that have so many simple enemies that it really makes this capacity worth it, but it should be noted.
Eidolons resurrect your party members, which can be very useful in the main story line.