Instructions
Ride the second swinging platform all the way over to the left of the screen. A brown section will slide out from the wall. Jump to it, then quickly up to the blue platform above, to collect the fist Star Coin.
Ascend the three swinging platforms, making sure to stay to the right. It looks like the right-hand path dead-ends, but there's a secret area past the false ceiling. Wall-jump up to the hidden blue platforms inside and grab the second Star Coin.
Stay to the right after you pass the halfway flag and the random item box above. The right-hand path splits off into two smaller sub-paths. Ride the swinging platform to a point from which you can jump to the wall of the larger of these two sub-paths. Wall-jump up the narrow shaft, and the Star Coin will be waiting for you at the top.
Tip: The seemingly open space in the top of the smaller sub-path is actually an invisible block. Hit it to release a 1up mushroom.