The Harpy Queen's attacks almost exactly like a regular harpy's, but her large size makes them slightly harder to dodge. If one chases her to the top of the stage, she may be almost unattackable for many melee characters as she will occasionally fly out of harm's way. Her large sum of health isn't going to help either.
The Harpy Queen has a Danger attack, where she shoots out sharp feathers out in different angles to the side and beneath her. It can be avoided by sprinting directly below her.
After she has lost enough health, the Harpy Queen will fall to the ground and remain there and become vulnerable to attacks for a few seconds, before she shoots back into the sky to resume her attacks (unless she has "Fall Recovery", which then she will instantly shoot back up).