@jokergeist: I don't believe so. However to my knowledge cat woman isn't in Bruces tier. A few comparisons off the top of my head would be how batman stalemated shiva where as shiva dominated cat woman with one hand, batman stomps nightwing (the most skilled robin) where as cat woman lost to tim drake.
Maybe I haven't seen the right showings for cat woman but her best skill feat to my knowledge is beating wild cat. I feel Shang chi could replicate that.
@jashro44: I think she's gotten the drop on Batsy a couple o' times. I can recall Catwoman giving the Justice League a good fight too.
I recall seeing scans of batman chasing her around Gotham where she showed some nice agility all though she was playing head games with him if memory serves (she was doing things like kissing batman). The justice league showing was a fantasy of cat womans.