Your first objective is to decrypt the radio transmission used by TYGER guards. Batman will automatically get out his Cryptographic Sequencer and all you have to do is hover over the bruise-coloured circle in the top-right and hold the A/X button (remember this, because it'll come in handy for the Riddler missions). Once you do that, another small cutscene triggers where it's further established that Catwoman is in serious danger. You'll finally get full control of Batman.
Run off the edge and hold A to glide. Since we're still trying to get that Critical Strikes upgrade before the courthouse, engage them in combat and try to get a 20x combo or higher. Don't be afraid to restart from the last checkpoint if you mess up, because you'll restart back at the top of the Ace chemicals building.
Once that group is taken care of, do the same thing to the group of inmates in front of the courthouse. You'll notice a large Batsignal in front of the courthouse; that's your objective marker that will guide you to your next destination. This fight, as far as this author can tell, is mandatory, and there doesn't appear to be a way to stealthily enter the courthouse without fighting this group of baddies. But no worries, you need that XP!
When you think you've done well enough, enter the courthouse.
The doors on either side of the main floor are blocked by inmates (though you'll get some funny dialogue if you try to enter that way), so the only way through is up the half-burned staircase in front of where you entered. Climb the stairs and you'll trigger another cutscene where Two-Face tries to pass judgement on Catwoman. When it's done, head right and up the ladder. You'll see a security inmate holding a gun; knock him out. You should have levelled-up by now, so hit Back/Select to enter the WayneTech menu and select Critical Strikes from the "Combat" sub-menu. Now you can drop down into the courthouse and begin the fight.
There's a good 50 enemies in this section, but most of them run away at the sight of Batman, and only 15 or so are man enough to stand and fight. Two-Face will taunt you from afar and try to shoot you. This author has never actually been hit by him (except the scripted shot immediately after the fight), and it appears to be mostly decoration. As for strategies for the fight itself, there's nothing new here except for the occasional enemy who will try to throw a crate or something at you, which can be easily countered. Time your button presses immediately after each strike to get Critical Strikes, which count as 2 hits on your combo instead of one. It's one of the best ways to get Experience Points in this game.
After the fight, Batman will finally be shot by Batman and another cutscene will trigger.