As you're sliding down, press X when prompted to jump over the gap. Open the green chest if you need it, then climb the stairs to the open area, where a Cyclops will show up, ready for battle. The Cyclops only has two attacks, one where he'll try to grab you and the other he'll just pound the ground. Rolling away from it will generally avoid both; Square, Square, Triangle will be your best move against it. Press Circle when prompted to slam his head against the ground if you want, which will release a few green orbs; if you do the Circle prompts, the third one will have Kratos killing the Cyclops.
After a short scene with Scylla returning to the game, you'll have to fight 3 Soldiers before the gate will drop. If you go down the stairs where the Cyclops came from, you'll find a Red Chest. Go inside the building and follow the path to the right, until you come to a giant statue of Poseidon. Hold down Circle in front of it to kick it away, revealing a hole that allows you to dive into the water.
Once you're underwater, go to the left and up the hole there, where you'll find the two Red Chests you might have seen when you first entered the building. Go back underwater and take the hole to the far right now, grabbing the Green Chest before if you need before going through the door. Kill the Soldiers that show up, then hurry and cross the bridge to the right before it collapses. Save, then head up the large ramp to the Temple of Poseidon.
