Erm... my instructions are probably gibberish, but here goes:
From the floor near to the large door at the end of the corridor, put on the helmet. Jump onto the white platform, then on to the stone platform on the wall.
Take off the helmet, and jump across the three brownish platforms that go back along the corridor. Stop when you get to the end of the three(?) and look slightly to the left where there's another stone platform. Jump onto it.
Put the helmet back on and some white platforms appear again. Use these to jump to another stone platform in the opposite corner of the large room.
Take off the helmet to reveal another couple of brown platforms that lead to the overhead cage.
Hopefully that makes more sense!