The key to this matchup is getting her to the corner, and in order to do that you have to be REAL PATIENT. No dashing, jumping, batarangs or calling bats unless you have frame advantage, or else you are going to get punished. Use trait bats to keep her honest; Only calling them and having them around should be enough to make her respect you and be more careful with her zoning, which opens you the possibility to walk forward. When she has trait on, pick your spots to call bats and punish her pillars with them; It is not going to be a big damage punish, but you must try to make her waste trait time, so she doesn`t gain as much meter as she could.
If you get close to her, pressure at will; she (along with some other characters, like Green Lantern or Doomsday) CAN NOT AFFORD to spend meter pushblocking you, because she does little damage without spending at least a bar. When you get her to the corner, pressure her and make her stay there ending your combos in B23, which gives a perfect distance to bait any way she has to escape.
I think there is a match between @
AK RM Blake and Glass Sword on youtube which shows (even though Blake lost by 25% health in match 5 of a ft3) the aproach you should take on to face her. It is 5 - 5 in my opinion, due to the overwhelming advantage Batman has in the corner, vs the little edge she has everywhere else.
I hope this helps!!!