I actually feel GA wins this match, but I haven't played that many Hawk Girls.
From far there isn't much Hawk can do to GA other than fly and throw projectiles. At this point, I just load up on ice arrows and try to snipe her out of the air or while landing. You are bound to hit her at some point and there isn't much risk invovled. Just do jump ice arrow or back ice arrow. When I hit her, I dash up and do b3, dash, sky alert, d2 xx ice load, 223 xx arrow (hold) dash up and continue f2d13 / b2 pressure in to new frozen arrow (either comboed or low/high if they block).
If you are in the lead, and Hawk is still content on flying and throwing projectiles, I suggest switching to fire arrows and keep sniping. Every hit does good damage and leads to a knock down. I would say that frozen arrow is by far the most important arrow in this matchup though, as Hawk's up close pressure can be pretty tight, and therefor a stray d1 xx arrow leading in to a full combo with set up, is awesome.
As for her corner pressure: d1 xx ice arrow, and if she blocks it, don't be affraid to push block to get out of the corner. Also use corner interactables or MB corner interactables.