Thought I would bump this back up...
You don't have to go as far around as the the vertical sword blade.
Use the ladder, double jump to the next platform. Cross the rope but don't go any further on the second rope.
From the corner where the first rope ends, face the horizontal sword (which is on the other side of the castle thingy) Levitate bounce up then PSI Float over to the horizontal sword. If you did it right, you should just grasp the edge of the sword and hang from it. You might hit the archway that's between the rope corner and the horizontal sword, but you should still be able to make it the edge of the sword. Climb up onto the horizontal sword. Don't go on the rope which leads to the vertical sword.
Instead, Levitate bouce up to the castle corner above the horizontal sword. There's a flat space up there.
Once you're on the flat area, Levitate bounce up over the roof and you should land in the center of the castle/drawbridge area. From there you can bounce up to either side of the castle thingy and Levitate bounce up and PSI float to either free-standing tower. One tower has a helmet power up (for health) and from the other tower you can TK/move the thing jamming the gear.