Jump towards the palace that's visible in the background. Grab a high platform and use it to jump and glide to the left one. When you're on the higher level, you can go back a few steps ("towards the camera") to grab a Gorgon Eye. Next, jump to the platform with green orb chest on it, and finally to the palace entrance.
Use the lever to the right of the central ramp. There's a difficult battle here, with some Cyclopses and small goblin-like soldiers. Focus on the latter, defeating them by performing throws. There's also an archer here - let him be until you deal with all other enemies, as he will respawn endlessly.
Grab a lever on the right side and rotate the mechanism to the left. When you reach the end, grab the next handle and continue until you reveal a passage. Once inside, use the lever and the walls will start to rotate. Looking from the left, get inside all of the surrounding rooms and grab the items from the chests. The most important item - Crank Handle - can be found in the first room. When the fourth room is revealed for a brief moment, pull out a movable stone pillar to block the mechanism. If the imps give you a hard time here, use Chronos Rage to put them down.
Go forth and turn left at the junction. You'll reach a rather big courtyard, which is the central element of the whole palace. Go up the ladder and use Crank Handle on the turnstile. Use it and slow down time, then jump towards the back of the screen, taking advantage of the fact that flamethrowers are temporarily blocked. There's a Phoenix Feather in a niche near them.
Run to the end of the corridor and use the lever. You now have to quickly return to an air vent that you passed, spread your wings above it and glide above the grate before it closes again. It's not easy and you will probably have to try it a few times. A good advice is not to wait until the air raises you, but head for the gate as soon as you spread your wings.
When you reach the room with some dogs and soldiers in it, defeat everyone and go through another gate. Destroy a scaffolding and push the stone block to the next room.