After the first cutscene, you should be looking up into Hugo Strange's smug, shiny face. When the lights come back on, wiggle the left analog stick to escape. It's a sort of gentle back and forth movement, which you should time with the swaying of the chair. Once Bruce has fallen over and the alarm activates, a TYGER Guard will walk in. When prompted, press Y/Triangle to counter his kick. The game will take over from here, as Bruce steals an encryption key from the guard, and is then beaten up by a second guard.
When you regain control, move into Line A (the line with only two people in it) and walk forward. Another guard will subdue you, and Hugo Strange will continue to gloat evilly in your general direction. You'll have a short conversation with Jack Ryder before the door opens, and inmates will jump over the fence to attack you.
Be on the defensive for this fight, as it's much easier to simply wait and counter the inmates' attacks when you're still in handcuffs. The inmate attacking Jack Ryder, however, goes down with one press of the attack button. Once Ryder is safe, press A to help him, and there's another partially interactive cutscene where the Penguin stomps on your face.
Now it's the Penguin's turn to gloat. Get ready once Penguin puts on his brass knuckles. As soon as he's about to attack, press the Counter button to break his arm, and your first real group fight will start.
You start the fight in handcuffs, and the attacks here won't count towards your Experience Points, so don't be afraid to miss a few. Once Bruce breaks free of his handcuffs, the real fighting starts. Use the same strategies that you did with Catwoman's level, although this time you won't have access to the Stun move just yet. Once everyone's unconscious, you can go and give the Penguin a nice smackdown. To the left of the Penguin is a ladder. Climb it, then jump the gap and climb another ladder. Bruce will contact Alfred, asking for a dropoff of the Batsuit.
The Ace Chemicals Building should be right in front of you. Jump towards it and shimmy along the ledge. Continue shimmy and climbing while Bruce and Alfred chat about plot-related things. Eventually you'll hit another cutscene where the Batplane finally arrives with your trusty suit. Climb up to the roof and press A/X to put it on.