Pre New 52 for both (obviously)
Abandoned factory, with equal parts lightened and dark, two-leveled with several large crates scattered throughout, with perimeter landing between the ground and second floor but no ceiling. Several "gargoyles" between perimeter landing and the second floor ceiling.
Battle will not leave the factory.
Morals on; Cassandra is not looking to kill, but will fight as hard as it takes to beat Bruce.
Both are looking to incapacitate or force the other to submit by any means, within character. (See above line).
No outside help, including the bat swarm. Strictly one-on-one.
Fight may shift between hand-to-hand and Arkham-esque predator (I dont know if theyll think predator combat will be effective, but if you can argue for it so be it).
GEAR AND PREP:
All canon knowledge of and experience with each other remains.
No prep for either combatant (Seriously, giving one character prep is stupid and counterproductive).
Standard gear for both; anything shown to be kept on hand on a regular basis. (Including sonics and exploding projectiles plus batarangs, grapple guns, etc).
Encounter begins with both characters 30 feet away from each other, both in dark areas.
Can Cassie beat Batman? Will the Dark Knight prove to be the best Bat there is? Scans are crucial, of course. And explanations are mandatory, no "...curbstomps". Thats childish. Any plausible pysche manpulation is welcome. I did check the forum for a one-on-one battle like this. I didnt see one but in the likelyhood that it exists, link and lock me. Have at it!!!
EDIT: Cassandra can talk but still has semi-pre-cognition