Praise the sun. Our Dark Souls Walkthrough provides tips for surviving the adventure, a guide to the entire world, and hints for slaying bosses.
After you work your way through to the end of The Duke's Archives, you'll find yourself in a grassy area with trees and lots of the crystal giant enemies. If you head downhill along the slope, you'll find the entrance to the Crystal Cave area. It's not far at all from a bonfire that you should have by now activated in the archives, which is good because you won't be finding a bonfire in the short but dangerous cave area until you defeat its boss.
When you start forward, it's important to keep in mind that the platforms you're working along are slick and treacherous. If you simply proceed straight forward, you'll likely start sliding and you won't be able to stop yourself as you slide right into an abyss. Instead of letting that happen, watch for a platform that branches right from the main trail. Along that route, you'll see one of the crystal giants plodding toward you.
Defeat the giant and proceed along the trail he was guarding. Ahead of you, there is an opening with ice powder falling in small chunks from a ceiling and breaking apart on an invisible pathway. You can watch where the ice is falling and breaking apart to determine the location of the invisible path. You can head straight forward through that opening to reach a far ledge, which you can climb to reach a corpse. Check the corpse to obtain some Humanity.
Now it's time to backtrack along the invisible path, and this time to follow the trail that visibly leads down past a floating butterfly. You don't have to engage the butterfly. Just keep a moderate distance from it and it won't wake up to attack you. At the end of the highest ledge along that route, you can drop down to some darker rock and then head back to the right, with the butterfly to your left and behind you as you proceed in the new direction. You'll soon reach another wide gap with more of the falling ice.
Assuming that you're facing properly, you can walk straight across that gap to reach the ledge on the far side. It's nerve-wracking, but you'll be safe. When you reach the far side, however, you need to be prepared to fight one of the crystal golems that will come at you from the left. This fellow is a tougher one, with stronger armor, and he hits harder. However, the strategy for battling him hasn't changed. Just make sure that you're not so ambitious that you fall into the abyss.
After defeating that golem, continue along the trail he was guarding. You'll have to head along some more of the gravel-like rock and ahead, you should see more ice chunks falling and breaking apart along the path. Edge forward and make sure that you have a good feel for the path's location. Then you can drop down onto it and quickly turn around to face the area behind you. There, you'll see some of the glowing rare enemies that like to retreat upon sight. Quickly take out as many of them as you can and collect the loot they leave behind.
Now you can either continue in that direction to cross the gap ahead of you and find a Blue Titanite Chunk on a corpse, or you can turn around and start back in the direction you were facing when landing on the nearby invisible ledge ahead of the lizards. If you do decide to go after the item on the ledge, be careful because the invisible ledge is not a straight shot; it has a curve around three fourths of the way across and you'll need to follow its path carefully to avoid stepping off the ledge you can't even see. Given the relatively unimpressive nature of the item that you'll receive if you make the perilous trek, you may well decide it's not a trek worth taking.
The path leading away from where you found the lizards is a much safer one. It follows what essentially is a straight line. You should still proceed cautiously and let the falling ice dust show you where you're safe to step, but there's less to worry about. When you finally reach the far ledge, there's more good news: you've crossed the last of the cave's invisible paths.
When you reach the far side of that path, the area widens and you'll see a bunch of the clam enemies ahead of you. There's one sharply to the left, as well, so make sure that you don't let it sneak up behind you. These clams are easy enough to toast with fire or to hit with melee attacks from the sides and behind if you take them on individually. Just make sure that you don't get too close too fast or you'll have a few clams rush you and that's more difficult.
Once the clams are defeated, equip a two-handed weapon and remove your shield. Make sure that you have good defense against magic and physical attacks both, then head forward. As you descend, your arrival will trigger a second fight with Seath the Scaleless, the dragon who you fought before being jailed in the Duke's Archives.
Seath the Scaleless
Though your previous encounter with Seath may not have ended well, this encounter in the Crystal Cave doesn't have to unfold the same way. As the fight begins, you'll see a crystal object ahead of you. Before you can start toward it, Seath slides down the slope behind you to attack. He clearly doesn't want you hacking apart that crystal device.
Quickly turn around once you are given control and run away from Seath, toward the crystal device. You should be able to hack it apart and when you've done that, it will be possible to finally harm Seath. Keep in mind that each time you battle Seath, you must start the fight by destroying that crystal device (which is behind him when you make subsequent attempts) or he will just heal any damage you inflict.
Seath has a number of attacks once the proper fight begins. While none of them are especially powerful, they do have an unpleasant side effect: they can curse you. The main thing that you absolutely must do is avoid letting yourself be cursed, or you'll die an instant death and then have to use a Purging Stone. While you can get more of those by battling the clams in the area ahead of the encounter with Seath, it's still an unpleasant situation. Reduce the likelihood of falling victim to that status ailment by equipping the Cursebite Ring, if you got it in the New Lando Ruins, and most or all of the Havel armor set.
To avoid being cursed, you'll also want want to keep a careful eye on Seath as you battle him. You want to hit hard (hence the directions to unequip your shield, so you can use two-handed attacks) and be ready to retreat. Most of his attacks won't hit you if you are close to him (or better yet, his tail), but occasionally he'll charge up a move and then send out a field of ice crystals in a radius around him. Those ice crystals will curse you if you don't get out of their way, which means running away from Seath's body and toward the edge of a cave (where you will probably also want to heal). You need to be ready to make that run at any time, and obviously your equipped gear will make it easier to do so. It's not worth staying in close and getting in an extra hit or two if that winds up leaving you unable to get away in time.
As long as you get good at avoiding the crystal attack, you should have a fairly easy time with Seath. When he's not charging up to hit you with crystals, his attacks are largely ineffectual and you should be able to get in a few hits before you're forced to back away to avoid being cursed. Then you can return to his side and resume your attack. If you have an especially powerful weapon, you will wear him down relatively quickly and win the day.
Once you defeat Seath, he'll drop the Bequeathed Lord Soul Shard and a bonfire appears. You can use it to warp out of the area. You may also wish to backtrack to where you originally fought Seath in the Duke's Archives to obtain the Large Magic Ember from a chest (and the Soul of a Great Hero from a corpse positioned along the upper balcony in that chamber). You can also revisit Big Hat Logan, in the side passage near the area's second bonfire. He taught you sorcery skills, but once you defeat Seath he will become an enemy. Talk to him, then kill him to learn the White Dragon Breath sorcery and to pick up a Big Hat and Tin Crystallization Catalyst.
With those activities completed, you're truly ready to continue your quest. Though first, you may also want to farm the nearby clams for precious Twinkling Titanite, now that you have a bonfire right next to them. Most of the best weapons at this late stage in the game require that material, and this is your best opportunity to acquire it.