World 1: Mid Castle

Coin 1 (before checkpoint)

When you reach the first swinging platform, leap from it to a platform that extends from the left wall, then onto the platform above for a coin.

Coin 2 (before checkpoint)

Upon reaching the trio of swings, use them to reach a platform in the top-right corner, just below a hidden shaft

Coin 3 (after checkpoint)

Shortly after the checkpoint, you'll reach another swing just below two shafts--the coin's in the right one. To reach it, leap toward the left wall of the right shaft as the platform swings to the right, then wall-jump into the alcove above, where the coin is.