A Cyclops will appear at the beginning and there are also eggs sitting on the ground, some of which contain more enemies. After all enemies are killed, a gate on the right side of the area opens up, which has a movable block. Move it out into the open, then turn the gear and ride the platform across. Follow this path to another area, grabbing the Red Orb Chest and Archimedes' Treatise Artifact on the left side.
Grapple the chain in front of you, then create a clone to hold it in place when you drag it back. Drop down the opening and grab the Gorgon Eye and Phoenix Feather, then turn the gear to open up the big gate. Grab the movable block and bring it to this area, placing it in the opening next to the gear. Turn the gear again to make the debris catch fire and then sizzle out.
Move the block all the way back to where you first got it, then use the Amulet to heal it so it catches fire and lights whatever is above it. Remove the block and place it in the receptacle to the right of the first gear (break the wood in the way) and turn the gear to make the thing fill with oil.
Bring the block to the area where you first caught it on fire, but put it in the middle of the two White Chests, using the Amulet to heal it and finally igniting the furnace. Go back to the previous room, where you'll fight a Gorgon and some Satyrs with Slings. Kill them, then turn the gear and use the platform to get to the upper area.
Some Manticore Hatchlings will appear, so kill them and use the vents to reach the central pillar, where you'll ride an elevator to the top. Jump across the gap, being mindful of the fire spewing out and then grapple and climb to the conveyor belt above. Go with the conveyor and jump over the obstacle to find two Red Orb Chests, then go the other way and turn the gear there to halt the conveyor.
Go back and about halfway through, two fire barriers will appear, as well as a bunch of enemies. You need to be quick here, as the barriers close in on you, so feel free to use any of your magic if you have any (you already have the Fire of Ares one), as well as grabbing and throwing them with Circle. If you're quick enough, then the fire barriers will disappear.
Go to the moving platforms and navigate past them all (you can on the rotating object in the middle for the second set), grappling the green point at the end to reach The Shoulder of Apollo.
