After the death of Hephaestus, go to the Hyperion Gate that leads to the chamber of Aphrodite.
A new power within the Nemesis Whip will be unlocked. Press R2 to try it out on the Sentries that Athena will summon.
Back to the Upper Gardens, go to the broken mechanism that you spotted before. Use the Nemesis Whip to get the mechanism working again.
Now cross to the other side and the open the big gate. We’ll solve some puzzles around here.
Start off by aligning the catapult to the left Hyperion Gate. Launch the catapult and climb through the wires. Open the red chest.
Go back down and head to the right side of the room. In between the pillars will be a lever. Pull it and the platform where the catapult is, will rise.
With the platform raised up, align the catapult on the gate to your north. Fire the catapult and the door will open. Look to your right and you should see footprints; use Hermes’ Boots to go to the upside down orange Hyperion Gate. You will find yourself in the upper level of the room above where the gate you just opened. Pull the lever and two treasure chests will slowly go down. Immediately go back to the catapult and fire it.
The two chests can now be open. Inside of the two chests should contain the Daedelus’ Schematics and a Phoenix Feather.
Before proceeding to the next area, align the catapult to your left and fire it. Use the wires to get to the chest that’s located to the upper north eastern floor. Open it and you will get a Gorgon Eye.
Use the rope that can be found north where you opened the door with the catapult. You will see another treasure chest here that will contain another Minotaur Horn. Now continue finding your way out.