It's not the only game I've played with this scheme but there's not a lot of them. The attack patterns actually aren't that hard to figure out, though, so even someone like me, with no talent, is generally able to get through.
The best thing to do with the Harpy is, like a post above said, take the egg to the face. Honestly, the cats are fragile and their strongest attack has a windup; especially if you have a lance or bow they're super easy to beat.