After finishing them off, walk towards the disgusting twin and kill it. Next, walk towards Castor's corpse to retrieve the Amulet of Uroborus. First, target the glowing rubble in front of you then press L2 to activate the amulet. Turn the right analog stick to the right to “heal” the rubble. Just hold it in that direction, enough to re-arrange the rubble into a platform that you can hop unto.
Jump to the platform to the left then run towards the screen to find a red chest. Now backtrack a bit and step in front of the ledge so you can activate the amulet and restore the bridge. Jump on the bridge and follow the path as it curves to the left. Here you'll find a decayed chest that you can restore using the amulet.
Delphi Passage Decayed Chest
Head to Aletheia for a scene. After hearing the oracle's dying words, continue forth and jump across the chasm. Scale the wall to the right first as it leads you to a secret cavern containing a Phoenix Feather.
Delphi Passage Phoenix Feather
Exit the cavern and scale the wall to the left. Jump to the aqueduct below and follow it until you reach outside. Continue past the Poseidon gate and kill all enemies. Proceed down the aqueduct and stand on the broken edge. Use the amulet to restore the aqueduct and create a passage. Continue forth to the Cistern.