Catwoman is a pretty straight forward battle, but will be a nuisance for some as the latter part of the fight will require some quick reflexes. I'll break the fight into parts as the fight is basically the same order every time.
Equip the Blackest Night suit if you have it to basically have unlimited chances to counter her attacks as you will be impervious to damage.
Part 1Counter her attack (

), then cape stun (

), followed by mashing
Part 2Dodge under her leap

+

,

, then cape stun, then mash
Part 3Counter her three attacks with

, cape stun, then mash
Part 4Now the annoying bit. As soon as you see her red eyes appear, hit

to counter, then cape stun, then mash
Part 5Again, counter with

as soon as her red eyes appear. This time you must counter 3 times in a row without missing, then cape stun, then mash
Part 6This part is even more annoying. Catwoman "phantoms" will leap toward you, if you counter the wrong one you will suffer a hit. Wait until you see the blue lines appear above her head ( I hope you're playing on normal), then counter with

followed by two more quick counters, then cape stun, then mash
Final PartThis is an exact repeat of the previous part, do it again and you've won the fight!
Here is a video for reference, take note he is playing on hard mode.