The boss of the Wing Dungeon is Head Thwomp. This boss is a large, stone block with a face that moves up and down, trying to crush Link. The room has four holes in the corners. To defeat Head Thwomp, you need to use your Roc's Feather to jump into one of the holes when Head Thwomp is directly above it. This will cause Head Thwomp to fall into the hole, flipping it over and revealing its vulnerable underside.
Once flipped, quickly attack its underside with your Wooden Sword. Head Thwomp will then right itself and resume its pattern. Repeat this process, being careful to avoid its crushing attacks and the small enemies it sometimes spawns. After several successful attacks, Head Thwomp will be defeated, rewarding you with a Heart Container and the second Essence of Time, the Ancient Wood.