Speaking from the side of HG, you have to be patient against air mace shit and not try to make random jumps or dashes at fullscreen. Try to block and dash after downwards mace while watching out for EX (Easier said than done, I know) until you're within healthy range to hit her with a jump-in. At that point it becomes a mixup between her trying to preemptively stuff a jump attack with fly normals or dive kick, move forward and out of your range or beat shit with air mace charge, or get down and escape with EX air mace or dive kick. At this point if you aren't going to risk jumping immediately b/c of retribution you need to wait and see if she does fly 2/mace charge/or EX air mace/or dive kick in an attempt to escape or hit you and respond appropriately . This is EXTREMELY important, the most important part of the matchup for almost every character in the game. Whiff punish with jump into float combo for the first two. If you block EX air mace she's at + but outside of mixup range, so be smart and don't panic, but if it whiffs you should get free ice spike if not slide (I'm not sure about the latter). Dive kick is punishable if she does it above minimum height, you need to be extremely fast though. Sometimes she floats after so I'd advise confirming 111 xx w/e or whatever float combo or appropriate punish KF has. Note that she can technically only fly for ab0ut 8 seconds, if you've been turtling fullscreen this entire time try to keep track of the time and see what she does, punishing with ground spike or super if you have it. I'd argue the latter is worth it, because most characters have to fight Hawgirl on her own grounds in a shitty war of attrition where both sides typically do mediocre damage.
As for dealing with ground mace charge and wing evade stance: You bait these by jumping neutral or back. Ideally backwards b/c her d2 is an amazing AA, but you can only punish WE 2 (The flip kick overhead) by neutral jump or making it whiff by walking backwards (Not backdashing, the recovery on whiff is far too good). Unfortunately the latter "loses" to mace charge and WE 3 (The fast fucking horizontal flying kick that's like -1 on block with really fast recovery) which are both 100% safe on block. Both options lose to backwards jump and reacting with a jumping move with a strong crossup hitbox. Both options are also her only wakeup attacks so be aware of that. These all work if she does this by cancelling from d1 and other moves/strings too, I highly advise using record mode in training mode to get a feel for this. On that subject, if she fly cancels normals, you generally get a free d2 or jab into combo, but you need to be fairly quick on the uptake and these often lose/trade to the MC and WE cancels, and divekick will hit you if you're slow or try to crouch jab her.
One last thing: if she has full bar, a life lead, and you can't afford to eat a super DO NOT FUCK AROUND. Don't jump, don't whiff, don't bother trying to punish fly landing recovery if you aren't 100% sure you'll hit her out of the air (She can cancel the recovery into super immediately) and while I'm not sure but she might be able to punish ice spike on block, at least within a certain range. It's not quite superman fast but it's still got range, speed, and the hitbox to mess you up for screwing around. Also for god knows what reason it's overhead even though it looks like a grab... not that I'm saying this should be one.
Edit: I forgot to mention that while getting in, once you're in the range where dashing will put you in divekick range you need to stop and just block instead. There's a sweet spot in between the air mace and her divekick where you can safely crouch without giving up ground, but you need to pay very close attention so that she doesn't adjust her spacing a bit, dropkick your head, and ruin all your hard work. Also you can tech roll divekick on hit so that she doesn't get hella advantage and wakes. If she lands sweep and dashes you basically need to guess 3 ways + throw, since she can dive kick, crossup divekick, or sweep again and none are escapable except with wakeups.
