Head north – you can take the tunnel, or go up the stairs and drop down, as you wish. When the Golem finishes talking, carry on north and go through the door. Step on the switch in here, then go back to the beginning of the stage. Take the stairs up, and jump across the floating platforms to the upper door at the north end of the room. On the other side, stay on the ledge and head round to the floating platform. Jump over to it. Now, you can't jump from here to the next ledge, so throw your chain at that pillar: you'll pull yourself, and the platform, over to it. You can make the jump from here. Head round to the south, jump across the smaller gap, and then round via the two platforms to the west exit.
In the next room, you want to jump across the platforms and ledges to the west. Your first jumps should be west, west, south, and from there west to the end. Go through the door. If you want a green potion, jump across to the east door, go in, down, and in, kill the golems, smash the chest, and then return here. Now jump across to the ledge to your north, and kill the lizard-man for a life extension. Return to the first ledge, and walk along it to the western end; jump via the platforms to the west ledge, and take the door.
In here, head over to the point at the east side where the ledge juts out into the room; there's a staircase up to it if you're on the lower floor, and platforms lead over to the west. Take them, and the door at the end, and smash the chest in the next room for a heart. Then return to the same spot, and this time head south to the other exit.
There are a lot of golems in here, and not much space to move, so be careful. If you get stuck on one of the green turntables, use your Throw-Chain to pull yourself off. You want to head round to the northeast side of the room, where there's another exit.
This room is pretty tricky. The simple way is this: run down the ledge along the west wall below the door, and hop down and to the right round the corner, then jump over the gap to the east. There should now be two floating platforms to your south, one of them right up against the ledge you're standing on. Stand facing it so that you're lined up with the right-hand side of it, and use your chain: it should pull the platform slightly towards you and slightly to the right. Move right yourself and jump onto it so that you're only half standing on its very right-hand edge. Now, if you face east, you should be able to pull yourself across to the wall with your Throw-Chain. You should then be able to hop south to the exit with ease.
On the other side of the exit, you'll find yourself in a large room with the boss music playing. Head over to the top right and talk to the upper left of the two statues.
When you've talked to the statue again, take the door. Back in Neugier Castle, head left and up the stairs.