The mini-boss of the Wing Dungeon is Swoop, a large, bat-like creature that flies around the room. Swoop will periodically dive down to attack Link. The strategy here is to use your Roc's Feather to jump over Swoop as it dives, then quickly turn and attack its back with your sword. It's vulnerable for a brief moment after its dive attack.
Swoop will also sometimes fly high and drop bombs. avoid these. The key is timing your jumps and attacks. Don't get greedy with your sword swings; one or two hits and then prepare to dodge again. After enough hits, Swoop will be defeated, granting you access to the chest containing the Roc's Feather.