I can help you out, if you can just let me know which time you are trying to beat her. The first time in the carnival or the second time in the To The Top of the Tower mission?

First time make her do backflips until she stops then hit her second time get on top of the truck and use the water gun-that yellow lokking thing

For the Big Top fight. FOLLOW her at close-ish range till she stops and looks drunk. Beat the piss out of her until she repeats the flips. At one point, she will jump to the other side of the top, RUN to her before she fills u with lead (Old timey saying i learned, meaning she kills you with her gun.) . When her HP is low, she will do that twice before she stops and looks drunk. Beat her up there.

For the Tower fight. You really do not get to lay a Batarang on her or Joker, just kill the Heli when It appears. IT'S TOUGHER THAN IT LOOKS! STAY ALERT! (Caps are to show importance, not to yell.)