Boodendorf
Bird woman!
Here are the matchups I think are in Hawkgirl's favor:
Hawkgirl vs:
Killer Frost (8-2)
What can KF even do against airborne Hawkgirl? Nothing. She'll probably try to slide under you but you can punish that easily with a d3 if you see it coming, and you can just hit her out of her airdash with flight 1/horizontal air mace throw.
Bane(5.5- 4.5)
Even with venom, if you guess correctly and flee to make him run out of venom, he'll be easy to beat. He got options to get in though such as his charge or his jumping uppercut. Especially once he has venom you have to be very careful.
Grundy(6-4)
His best tools against zoners, ex swamp hand thing, will NEVER EVER hit you, flight completely negates this.
Superman(5.5-4.5)
Your zoning >>>>>> his zoning, he'll have to make his way through your maces and will be forced to rushdown, we all know how good Hawkgirl is up close too so it's tough for supes, though you'll have to watch out for his upward grab once he's under you, and his pressure is particularly safe with super breath. It's all about being patient.
Sinestro(6-4)
His zoning beats yours, boulders > flight at full screen, but he can't handle Hawkgirl's rushdown. It's easy to get close to him too thanks to we3 and mace charge. And as soon as you're like at 3/4 away from him, you can punish any zoning attack you blocked with reversal mc.
Harley Quinn (7-3)
What can Harley even do against Hawkgirl zoning her from fullscreen? Nearly nothing. You'll shut all of her options just by zoning and staying in flight. Just make sure you stay out of the angle of her anti air gun.
I haven't fought enough of the other characters to know the mu, all of those are based on my experience.
Hawkgirl vs:
Killer Frost (8-2)
What can KF even do against airborne Hawkgirl? Nothing. She'll probably try to slide under you but you can punish that easily with a d3 if you see it coming, and you can just hit her out of her airdash with flight 1/horizontal air mace throw.
Bane(5.5- 4.5)
Even with venom, if you guess correctly and flee to make him run out of venom, he'll be easy to beat. He got options to get in though such as his charge or his jumping uppercut. Especially once he has venom you have to be very careful.
Grundy(6-4)
His best tools against zoners, ex swamp hand thing, will NEVER EVER hit you, flight completely negates this.
Superman(5.5-4.5)
Your zoning >>>>>> his zoning, he'll have to make his way through your maces and will be forced to rushdown, we all know how good Hawkgirl is up close too so it's tough for supes, though you'll have to watch out for his upward grab once he's under you, and his pressure is particularly safe with super breath. It's all about being patient.
Sinestro(6-4)
His zoning beats yours, boulders > flight at full screen, but he can't handle Hawkgirl's rushdown. It's easy to get close to him too thanks to we3 and mace charge. And as soon as you're like at 3/4 away from him, you can punish any zoning attack you blocked with reversal mc.
Harley Quinn (7-3)
What can Harley even do against Hawkgirl zoning her from fullscreen? Nearly nothing. You'll shut all of her options just by zoning and staying in flight. Just make sure you stay out of the angle of her anti air gun.
I haven't fought enough of the other characters to know the mu, all of those are based on my experience.