Because you and Bronze Tiger are confined to a makeshift arena, this is a very straightforward fight. The first phase is easy: simply counter Bronze Tiger as needed, then do a cape swing and pummel the stunned Tiger. The next phase can be confusing if Bronze Tiger is the first boss you're fighting, but once you know what to do, it's a cinch. When Bronze Tiger lunges into the air, quickly roll-dodge out of the way, if you don't, he'll land on you no matter what. When his claws get stuck in the floor, simply stun and punch him like before. The third and final phase is pretty much the same as the first (and plays very much like the introductory fight against Catwoman), Just counter three consecutive swings, then stun and wallop Bronze Tiger into a KO.