Once you get into the cave keep following the pipes until you enter a massive chamber. Walk across the pipes to the central pillar, and then climb down the chain on Ico's left. Once you are clear of the pipes, turn to Ico's left, and jump over to the central pillar. You will land on a ledge going around it. Walk around the pillar to the right, and cross the bridge on the far side to the outer wall of the chamber.
When you get to the outer wall, follow the path off to the left. Shortly before you get to your destination you will have to jump over a small gap. After the gap, above the ledge you're on, there is a track bridging the gap between the wall and the pillar. Climb up onto it and pull the car on it over to the outer wall as far as you can. Then drop down onto the ledge and walk under the track. Jump out and grab the chain under the track.
Slide down to the bottom of the chain, then jump at the outer wall to land on a lower ledge. Follow it off to the left, jumping over two collapsed bits, until you get to a ladder. Get onto the ladder, and immediately jump off it onto the bridge below. You don't have to jump off the ladder, of course, but it lines you up perfectly, which is handy. When you land, go to the central pillar, then follow the ledge off to the right to find another ladder. Climb down it to ground level.
At the bottom, go over to the walkway on the right and climb onto it. The way left is blocked by Idol Doors, and without Yorda you can't open them. Instead follow the walkway to the right, and go through the doorway into a cave. Go to the front of the boat in the cave to find the dock. To the left of it is a path leading up above the waterway. Follow this up to the Idol Sword. Go back the way you came to the large chamber and approach the Idol Doors.
The sword will open the doors, allowing you through. Go through to the elevator. Pull the lever to activate it. When it stops, open the Idol Doors and enter the Casket Chamber.
Written by Crumplecorn