When Bizarro III found himself infused with radiation from a blue sun, he developed the ability to replicate himself as well as create other "Bizarro" lifeforms based upon likenesses of people from Earth. He used this power to populate a cube-shaped planetoid dubbed Bizarro World within the blue sun star system. One of the many duplicates that he created was a Bizarro version of Hawkgirl. Bizarro Hawkgirl, working alongside her Bizarro confederates Batman, Flash, Green Lantern and Wonder Woman, sought to save Bizarro from Bizarro Doomsday by dropping their hyperbolic headquarters on top of him.
Exerpt from Scribblenaughts Unmasked: Looking similar to Hawkgirl this Bizarro member of the Bizarro Justice League has her wings as a part of her, rather than a flying apparatus she can wear.