World 3: Mid Castle

Coin 1 (before checkpoint)

When you reach the large spinning square (with an item box in the center), leap from its right ledge when it's at its highest point into a hidden alcove containing a door. Inside, you'll find the coin inside another rotating structure--leap from one of the high sides to reach it (just watch out for the ball and chain!)

Coin 2 (after checkpoint)

The second coin is also the seemingly trickiest to get--you'll find it at the top of the tall elevator shaft. So here's the deal: it's blocked in by some bricks, which can only be destroyed by the rolling balls that'll join you on your ride. However, during the ride you'll encounter two Pow blocks, which can and will destroy the spiked balls if they're activated, whether you throw it or the spiked-balls roll into it. As such, you need to make sure those Pow blocks don't go off when the spiked balls are rolling around. For the first one, just activate before the balls appear. You'll have to pick up and carry the second one though, being careful not to throw it until after the balls have rolled through the bricks at the top, creating a path you can use to reach the coin.

Coin 3 (after checkpoint)

To reach the final coin, just before the boss door, leap from the top of the blue spinning platform below, then wall-jump off the right wall to the short one on the left, then from there into the space above containing the coin.