You will see a time-slowing statue - push it to the end of this corridor. You'll see another translator commit suicide. Place the statue in a way that's shown on the screenshot below. Use the lever to open the gate. Go into the room and enter the magical mirror. You'll be transported a few seconds back in time. Slow down the time (L1+R1) and run towards the translator. You should be able to catch him before he jumps off the cliff. If you don't manage to go it, try once more. When you succeed, repeat the "interrogation" procedure. Take the Warrior's Skull and open the door.
Use the turnstile to open the air vent and glide above it to reach the lever. When you turn it, you'll empower the air supply. Use the turnstile once more, and this time the air will lift you to the ceiling. Go to the opposite end of the area and drop down. Use another turnstile to get back on the courtyard.
Two Cyclopses will attack you. When you defeat them, another two will take their places. It's not a difficult fight, as these monsters are quite slow and have limited range. Open one of the doors using the Warrior's Skull, and refill you health and mana. Enter the elevator and grab the chain in the middle to lower it. A group of skeletons will attack you - be quick about eliminating them, because if you take too long, you'll get crushed. Use your high-range magic spells here, preferably Chronos Rage. When you reach the bottom, you'll also have to open the gate manually - do it quickly or you'll end up dead.
Use the rope to get across the lava pool. Archers will bring you down for a moment - jump towards them and deal with all enemies in there. Especially watch out for gorgons! When you are done, jump back down and continue to the next room. In here you'll be attacked by a group of weak soldiers.
You'll notice a kind of archery target on the wall to the right (see right screenshot above). Use the bow to shoot it and you'll get a Phoenix Feather and a Gift of Magic (immediately raises your magic bar one step!). Use the wings to get to the upper level, near the huge, rotating cylinders. Fly past them, using the air vents below.