Just a small tip for doing beatdowns in this game: the combat mechanics in this game are slightly different than in the retail games. When you stun a thug with
, immediately start mashing
in order to get locked into beating him down - don't wait that extra split second for the cape stun animation to finish (like you would in the retail games).
Also, when you see that a thug is about to strike you, you'll have significantly less time to react to it than in the retail games, so be wary of that subtle but important aspect (these tips are especially helpful if you're trying to go for the "League of Shadows" achievement).
All that being said, I believe the tracker for how many beatdowns you've performed carries over if you reload a save, as I got this achievement before even apprehending Catwoman, while I was restarting the checkpoint before the fight with several enemies (while trying to get a x25 combo).
Good luck!