Flipswitch Galaxy is accessible from the Terrace observation dome. You need 7 Stars to enter.
This galaxy consists of a single planet, made up of three sides of a cube.
Painting the Planet Yellow
You need to touch each tile on the planet to turn them from blue to yellow. Each time you touch a tile it will flip between blue and yellow. Avoid the electric fences, the spiky edges of the moving platforms, and the pulses from the pink enemy up at the far end of the top side.
One method to change all tiles to yellow is as follows. At first, when you land on the first switch, go left and then, when the view changes, down. Go along the bottom, then onto the trap and right until you get to a yellow switch. Then go up, and when the view changes, around, turning the switches yellow. You should end up on the corner right of where you started. Then go down and hit the last switches, using the trap if you need to.
Once all the tiles are yellow, the planet will turn green and everything will be deactivated, including the traps and the pink enemy. Collect the Star by jumping on the pink enemy.