Sorceresses that can survive on hell difficulty

You cannot survive even Normal difficulty with a Sorc that focuses on one skill, at least not without help (and help is rare in D2 nowadays; most have moved on to D3). By the end of Act V Normal, you will have faced at least one powerful Cold-immune (Frozenstein, and Duriel in Act II also has high Cold resistance in Normal and is immune in NM/H) and several immune monsters in the gauntlet that you face when confronting Baal. A dual-tree Sorc is typically your best bet, and you can usually get away with select skills from all three.

As another answer mentions, the MeteOrb build is the best choice for a Sorc looking to be independently effective through Hell difficulty. This build maxes Frozen Orb, Meteor, Fire/Cold Masteries, and as many synergies as possible (mostly on Meteor; FO's only synergy is rather weak). You'll also want a decent hireling as a meat shield; the most common choice is an Act II Defensive merc, because their Holy Freeze aura will slow even Cold-immune enemies. The basic tactic is to FO everything that isn't cold immune, and Meteor everything that is. The trick is to lead the target with the Meteor; most guides say to basically cast it on yourself as you retreat, and watch them walk into it (for thousands of points in damage). Large groups of monsters with no immunities can be given a one-two punch of slowing them with FO, then slamming a Meteor into the mob (hopefully centered around your hireling and not you). High-hit-points enemies like bosses are generally handled by having your hireling toe-to-toe it with them while you alternate FO and Meteor. The biggest problem with this build is that both of your primary skills have a cooldown, which throttles back the amount of pain you can inflict over time. FO also has only one synergy (besides CM), and it's not very powerful, so you'll find that FO becomes much less powerful (relatively) beginning about Act V Nightmare.

Other variants on the "fire and ice" theme include:

• BlizzBall - Blizzard/Fireball combination. Cast the Blizzard between you and the oncoming horde, then follow up by tweaking Fire Balls on any stragglers. Advantages over Meteorb are relatively quick access to these "final" spells, serious DPS from Blizzard, a tweakable fire spell, and a large number of synergies for your "+X to All Skills" items. Biggest disadvantage is that you'll need more skill points than you get to fully buff all synergies of both final spells, so you'll have to choose between favoring fire or ice which will eventually hurt you either way. Get as many All Skills buffs as you can, and also bump casting speed as much as you can.
• Meteor Spike - Stick with Glacial Spike over FO. GS has a smaller area of effect and less total damage, but freezes non-resistant enemies completely for the fire from above, and because it doesn't have a cooldown you can tweak it in between Meteor casts. You'll want tons of Energy stats and + to Mana items for this build as you'll burn Mana very quickly; some casting speed improvements are always welcome, but the faster you tweak the more blue and purple potions you'll be gulping down.
• HydraOrb - FO/Hydra. Hydra gives you a 10-second turret spewing fire bolts at nearby enemies dealing up to 161 damage per bolt (plus bonuses from synergies, + to skills and FM). Advantage over Meteorb is less aiming required than Meteor, the ability to easily hide or run from large groups or powerful bosses while the Hydras do their thing, and the best overall build for dealing with spread-out groups like ranged attackers and fleeing monsters. The biggest disadvantage is Hydra's 2-second cooldown, which will also prevent you casting Frozen Orb. Coupled with FO's one-second cooldown, this build will put a hard limit on your cast rate. You'll probably find yourself simply spamming one or the other spell in any given fight, depending on the exact situation. + to All Skills, of course, casting rate and mana are less important as Warmth's boost to mana regen coupled with the cooldowns should keep your blue orb fairly full by the time you arrive at this combo.
• HydraSpike - Trades FO for GS on a HydraOrb build, giving you a zero-cooldown and thus "tweakable" primary ice spell to mix with the auto-turret fire damage of Hydra. Decent for crowd control, with the area-effect freezing of GS and Hydra's AI, it's best against high-hit-point bosses that you don't want to stand toe to toe with (which is virtually all of them); Start with a GS to slow their approach, cast a few Hydras, and run circles around them, keeping a group of Hydras going and re-freezing the boss every few seconds.

Pretty much all of these will give you a formidable build for Hell difficulty.

To this basic stew of fire and ice, you typically add two skills from the Lightning tree. Teleport (which requires Telekinesis) allows you to get around the map very quickly, including across chasms and moats, and is pretty much a must for boss runs (repetitively creating new games on B.Net to kill the same baddie over and over for item drops) including the popular Mephisto run, which requires exploring the largest single dungeon floor in the game (Durance of Hate Level 2, Hell difficulty). It's also useful for "kiting"; staying in front of a large, powerful enemy who has to get close to do the most damage. Static Field is also a powerful friend for enemies with high hit points and resistances; it takes a flat 25% off of the HP of any enemy in range that isn't fully Lightning-immune (think of an enemy like Diablo, with 1,000,000 HP, and imagine executing an attack that takes off 250,000 HP in one blow).

Now, don't go crazy putting points in either of these. Neither skill benefits much from maxing it; Teleport's mana cost goes down, while Static Field's radius increases. In building your character, you'll be looking for as many "+X To All Skills" items as you can get your hands on, like the Skin of the Viper Magi, an Oculus or Death's Fathom, and/or a Memory or Heart of the Oak runeword staff (Heart of the Oak, while expensive, is one of the few runewords that makes wielding a staff instead of an Orb and shield a smart choice), and in addition to buffing your primary skills, these items will give you a significant return on the one point each that you put in these Lightning skills.

I've seen Cold-Lightning combos work as well; FO/Nova is an extremely powerful crowd-control build, combining the slowing power of the Orb with a zero-cooldown omnidirectional lightning spell. Less powerful against bosses than Meteorb, because the cost per cast of Nova is too high to just be hitting one enemy for around 200 damage, and the nature and cooldown of FO makes it less useful against a single enemy. Chain Lightning, or just plain ol' Lightning, is also a popular skill to mix with a primary Fire or Cold spell, but I find these to be too temperamental; their minimum damage is 1, basically halving their average damage and making them very unpredictable, reducing your ability to "fire and forget" as you can do with most other spells.

Just remember that in Hell difficulty, virtually everything has at least one immunity, and the most common one especially in Act I is Fire. Focusing on a single skill tree is a sure-fire way to invalidate your build beyond Nightmare, but at the same time, a jack-of-all-trades build typically can't do enough damage to last long either.

The most versatile sorc build I've come across is the Meteorb sorceress (meteor and frozen orb). Whenever I start fresh on a ladder this is my first character. She can get through hell with minimal gear. Here is an example skill build for a sorceress starting nightmare: lvl 40 Meteorb Sorc

The dual elemental damage allows you to handle a majority of mobs with only the dual fire/ice immune giving you trouble. As Blem said, having a merc with good physical damage is key to handling these packs. If you don't have a decent merc, just avoid them.

As far as keeping her alive, make sure you pump vitality (no energy and just enough str and dex to use the gear you want) and use teleport liberally. You shouldn't be letting monsters reach melee range and you should keep as few ranged monsters in line of site as possible.

An important part of having a caster in nightmare/hell is having a good hireling to take out the once you can't yourself.

Personally I preferred frost (frozen orb or blizzard) build, then with 1 point static field you should be able to take out most packs, with frozen orb build you can even put some points in fire tree to cover all 3 types of damage, something like this, with some +skill can help your hireling.

That being said some times you should just ignore some packs and run around them if possible, the reward for killing a really hard pack that you can skip will most not be worth it compared to what you could have killed in the same time somewhere else.