These creatures are part of the same family as the Lizalfos and Dinolfos except they can fly. Look closely at the Aeralfos and his shield is actually a Clawshot target. Once it is ready to attack, it will hold its sword back and shield forward. Link can then use the Clawshot and pull the Aeralfos closer. Strike at him with several sword slashes and he'll regain his footing. After a short while he'll return to the air.
After this, the Aeralfos will fly around and leave through one of the windows in the room. This phase is nearly identical to the first phase, except the Aeralfos will fly in and out through the four windows in the room. He also floats a bit higher, which means Link cannot always Z-target him, so the Clawshot needs to be aimed a bit higher if he is too high.
Defeating the first Aeralfos allows Link to obtain a second addition to his original Clawshot; making them the Double Clawshots.