In front of the gate is a switch you can grapple, so do that and go backwards with it all the way, then create a clone to hold it in place. Behind you is now an open door with a White Chest and Red Orb Chest. Grapple the green point above the gate, deactivate your clone, and drop down into the next area.
Here, you will have to fight with two Empusas. They should be no problem after the battles in the previous. Once they're killed, go to the gap and use the Amulet to repair the steps, then go through the door at the end for a cutscene. Note that there is a QTE near the end, so make sure you pay attention.
