One other useful tip, she has no answer to staff mode d1.
No one does ;D
But seriously, I'm not sure if it's written here, but I did a longish set with my Hawkgirl buddy, and I have some notes on that matchup.
With staff, her charge-in move, bf2 I think, but I'm not sure about her move names, cannot be tagged by j2 very well, but it can be tagged by j1, so mid-to-close that move is awesome. She can't easily command dodge then dive between staff pressure strings if you mix up the amount of d1s. And his d1 is a great answer to some of her not-as-tight frametraps. When she's flying, the insane hitbox on j2 catches her, but she won't do that much flying above your head, mostly low-to-ground dives and faraway flight.
Escrima is what you actually want to stay as, I found, look for a d2 and if she does ground mace you can ground spark under it. His dashes are faster, too, so you can space yourself right, then when she jumps or tries something to get in, change weapons and chain that to flying greyson, and she'll hate her life, it either trades with her charge or you smack her pretty substantially for one hit. On a staff or escrima knockdown that results in her falling far away, switch to staff and have a seismo ready for her wakeup, then switch right into ground spark and play the spacing game.
Yeah, so a lot of weapon switching, a bit more than usual. Move in sticks, dive in staff, footsie in either, switch to staff then back to sticks for a fullscreen knockdown, is at least what I'm doing, and it worked pretty well once I figured out my plan.
Stage Note: A stage I never thought about before that is great for the matchup is the Port in Themyscira. I can't describe, but the barrels being on the ground and the mobility tool in the center are really helpful.
Opposite note: the asylums SUCK for this matchup. Staff mode dies to all those quickly-chucked interactables from the air, which seem to be good only for power characters, and Hawkgirl can snipe most of your jumps getting to those tvs in cell block.
Not sure a specific matchup for the number, but it's better than Grundy vs Hawkgirl, that's for sure. I also think it's pretty positive for Nightwing, though that is stage-dependant for sure.