A giant Titan is more of a level of his own than a character, at least for the time being. From now on you can glide using the Icarus' wings - just hold X when in mid-air.
You'll see a save point far in the background. Go towards it if you want to. Go up the Titan's nose and jump from one platform to another (use the wings) until you reach the entrance to some kind of organic cave. Defeat the enemies (flaming bats are easily dealt with by pressing O when near them) and pull a movable hunk of stone (bone?) towards you. You can use it to reach a niche on the left to get a Phoenix Feather. Now stand on the other side of the movable pillar (in the back of the screen) and pull it towards you, so that you can enter the next room and still use it to reach the upper platform.
A third and final Titan Minotaur will greet you in the next hall. This battle is a little bit different than the previous ones, because at a certain point of the duel, he'll hit the floor so hard that it will start to soak in lava. When it happens, grab the wall in the back of the screen and stick to it until the floor comes back out. You will have to jump from side to side in order to avoid enemy's projectiles.
When you defeat the enemy, it will transform into a solid rock. Move it in a way that will enable you to jump onto a platform in the back. Once you're up, go further and jump down to the left - there's a Phoenix Feather in a chest. Now, jump right and you'll reach a huge hall.
You'll see a save point to the left. Go towards it - attack the tentacles that hold a rock nearby and wait for it to get stuck on a little isle in the middle. Go after it and jump on it, then hit the isle. Press R1 in an appropriate moment to save yourself from falling down and jump to the other side, using the wings.
Destroy a piece of rubble in the next room to restore the air vent to its functionality. Spread your wings above it and you'll be lifted so high that with no problem will you reach the upper platform in the back. You'll find yourself in a corridor with a few bat nests. Destroy them all (it's easy to do that using the L1+X combo). One of them will reveal a ledge. Use it to grab a wall and climb along it, jump and fly to the opposite side, then reach the end of this room (you'll have to destroy a stalactite that's blocking your way). You should see Atlas' face far in the back. Grab a wall and go along the ceiling until you reach the cave entrance.
HINT: Destroy all the stalactites along the way and one of them will reveal a secret passage that will lead you to the Urn of Prometheus (see the right screenshot above).
Go further until you reach the huge room you've already been in. Go along the wall and ceiling to the opposite end, destroy some more stalactites and go on until the end, then drop down to the floor. Unlocked air vent will let you glide towards the exit, that leads to the Titan's giant hand.
Jump down to the nearest platform, then to a circle with a turnstile in the middle. Defeat the enemies and raise the platform using it. Jump further towards that Titan's hand, remembering to glide whenever necessary. Slide down the rope and climb the wall. Use the hooks to reach a stone platform.
You'll end up in an area with two movable pillars. Use the ramp to place one of them on the other, and then use them both to reach the upper level. Once there, you can jump along the wall to the lest and grab a Gorgon Eye.
Go further and climb onto the wall. There's a difficult arcade sequence before you. The idea is to jump from one side of the wall to another so that you don't get hit by the falling rocks. Don't be hasty and stick to the inner parts of each sides - it will make your moves more efficient. When you reach the top, you'll have a quick chat with Atlas, who will grant you a new power (Atlas Quake). Use it to defeat a group of weak enemies. After a while, the Titan will transport you back on the surface.