I'm in the West Chamber, and I can't get out. Any guidance would be helpful. I assume that I have to use the pettlecopter, but it expires before I can get out.
Have you just collected the Slipstream power and then there's the Helibud to the left of the shrine? If so you need to use slipstream to get back to the ledge on the far right. To use slipstream you need to draw a curvy long line (straight lines are treated as gusts which isn't what you want here). You'll need to draw a line that takes you to the middle of the room, then draw another slipstream to keep moving right and then when you're near the ledge you can gust onto it.
If you're feeling adventerous you can try going up the gap at the top in the middle for a secret