Stand on the middle white square just outside the room. Step on the brown square inside the room, hop back and side-jump to either side to avoid the rolling boulder.

Step on the same brown square, then onto the white ahead and finally on the next brown square. Three boulders will roll, but they will not hurt you.

Now step on the white square ahead and immediately side-flip to the right to avoid the rolling boulder. Side-jump back to the white square you came from.

Jump over the next brown square in order to land on the white square beyond. A boulder will roll, but it will not hurt you.

The brown square ahead will make a boulder roll in your path, so do not step there. The brown squares to your left and right side will also make some boulder roll, but they will not hurt you. Use these squares to enter the alcoves and use the two switches.