In this chapter, Batman goes after The Penguin, who has captured Mr. Freeze, the manufacturer of Joker's cure. Tortured police officers, pet sharks, a murderous zombie and trick umbrellas stand in Batman's way.
Now that you've successfully disabled all the disruptors, go back to the security console you couldn't hack before. Whip out the Cryptographic Sequencer and hack it properly. Proceed forward and turn left. Don't worry about that dinosaur, it's mechanical.
You'll be introduced to a new enemy type: a body-armoured thug who can only be harmed by a Beat Down (Stun once, then rapidly mash the Attack button). With these guys, it's best to leave them for last since you can beat them down without interference. Also keep in mind that your combo will break if you try to hit them with a regular attack, so pay attention to where you're aiming that analog stick. For this particular fight, it's fastest to take out all three enemies with Beat Downs: isolate one enemy, stun him then Beat Down, and if another enemy tries to sneak up on you, counter him. Alternatively, if you're not concerned about racking up experience points, the body-armoured thugs are also vulnerable to all of your special combos, once you get your combo multiplier high enough.
The starting method I used in the video is quite effective: quickfire the REC on the body-armoured thug and one of the other regular thugs, then go to town on the third. Repeat the process with the other two. Once all three enemies are down, talk to the undercover police officer that Penguin's goons were harassing when you walked in, then proceed into the next room.
Walk forward and Batman will point out a high, barbed-wire fence with a small gap at the top. Get out your Remote Controlled Batarang and you can guide the projectile to hit the switch on the other side. Once you've done so, continue walking forward into the arena-like room to trigger a cutscene. (For some reason, this section got cut out of the video, but I will do my best to get an improved version of this room up quickly).
This group fight has two waves. The first wave isn't particularly difficult, but it's long, and if you don't keep an eye out you can easily miss some counter opportunities. You can easily get a high-40's, low-50's combo if you rely on Critical Strikes and Counter when you need to.
The second waves is a fight against a Titan. The method for taking down Titans is different from Arkham Asylum: all you need to do is perform an Ultra Stun (a three-hit combo with the Stun button) then do a Beat Down. This will cause Batman to jump on the Titan's back. This controls exactly like it did in the first game, except now you can perform a Titan Charge with the A/X button. Focus on the Titan first and counter regular enemies if they show up to attack you. Don't focus on fighting the rest of the regular thugs until after you've taken out the Titan.
Once that fight is over, you'll have yet another switch to hit with the Remote Controlled Batarang. Throw it towards the electrified gate to the left of where you came in, through a small gap, and hit the switch on the left side. The far-left grille in front of you should open, and a conversation with Batman, Alfred and Oracle will trigger.
Move forward and there should be another grille on your left. This one is opened by a nearby security panel, so hack it with the Cryptographic Sequencer. The grille will open to reveal an elevator powered by an electric battery. Climb in the elevator and use the Remote Electrical Charge to ride up. After a while, you'll suddenly stop moving. Equip your Explosive Gel and use it to detonate the ceiling blocking your path.
Climb up and move forward to another weak wall, which you can also detonate with some Explosive Gel. After the fireworks, head to the door on your left.
Move forward and detonate the cracked ice with yet more Explosive Gel. Walk forward to trigger a cutscene of Penguin having his way with an undercover officer, using one of Mr. Freeze's weapons. You'll need to cross over the unsteady ice slowly, or it will break open underneath your feat and you'll be eaten by a shark. The fastest way to cross the ice is to crouch walk by holding RT/R1 and move the analog stick about 80% forward, just enough so you can move quickly, without alerting the sensor that Batman adds to the heads-up display. Free the cop who was being tortured in the last cutscene and head down toward the ice again.
On your left there should be a raft-like platform being held in place above the ground. Bring it down to the thawed ice with your Batclaw, tapping A/X to pull it down. You can then use it as a raft to rescue the other two police officers encased in ice. Use Detective Mode to find them.
Climb the ladder near where you rescued Officer Strickland, and head through the corridor on your right. Turn right again, then head through the door.
Your next big Predator section is coming up, and this time you have to deal with a new enemy type: thugs with thermal imaging headset who can spot you hiding from a gargoyle. While there is an upgrade to counter this (as long as you're standing perfectly still, that is) you don't unlock it until much later in the game. As it is, you'll need to move quickly from gargoyle to gargoyle.
Once again, the best method for this fight is to take out isolated guards, and make the group near the hostages spread out. It's good to start with the guard right next to Freeze's suit, and then the guard on the lower floor. From here on, just be patient and take out the remaining guards one by one. There's no need to rush in, fists flying, especially not when everyone is armed. When you're down to one enemy, it's safe to use a Glide Kick from a gargoyle to stun him, then knock him out with a Ground Takedown.
Once all six hostiles are taken out, talk to the cops, and then backtrack towards the Torture Chamber again.
Torture Chamber part 2
When you reach the ice floes again, you'll want to head toward the room straight ahead. Cross over to the ice with your raft, then walk carefully over to the balcony. Grapnel up there and you'll see a group of enemies taunting you. If you approach them, a gate will appear out of nowhere, blocking your path. Use the Cryptographic Sequencer on the security console on your left to deactivate the gate, then fight the enemies. It's the same composition as last time: two regular thugs and a body-armoured thug. When they're down, go through the door.
Move forward and you'll find Mr. Freeze encased in a display box. Try to use Explosive Gel on the wall to your right. SURPRISE! It's the other Abramovici twin. Instead of using a hammer, this brother has a sickle. Subtle.
Use the exact same method as with the other Abramovici twin: Beat Down on him mercilessly, double-tap A/X to evade when he or a regular enemy attacks, repeat. You'll be able to get a 50 hit combo from him alone. Once he and the other cronies are down, go through the area where that wall used to be and hack the security console behind Mr. Freeze's exhibit to trigger another cutscene, where Mr. Freeze tells Batman about the security override for his weapons, hidden in his suit. It's time for more backtracking to the Armoury!
Torture Chamber, part 3
Use the same method as last time, only backwards.
Armory, part 2
Talk to the cop near Freeze's suit to activate a cutscene, and Batman will acquire the Freeze Override. Head back to the Torture Chamber one last time.
Torture Chamber, part 4
The ice should have completely thawed on the right side, towards the Iceberg Lounge. Take a raft over there. It seems uneventful until suddenly, Penguin's pet shark grabs a hold of the raft. Give that shark the old what-for. Continue on your merry way towards the Iceberg Lounge, and zip up there with the Grapnel Claw. Head down the corridor and go through the door.
The Penguin will fire the Freeze Gun at you out of windows. You need to stay behind cover to avoid getting hit. Move left around the room until you reach a catwalk leading right to the Penguin. Equip the Freeze Override (called a Disruptor in the inventory menu) and use it on the Penguin. Approach him and press X to uppercut the arrogant blankety-blank into next Tuesday. The next cutscene, however, shows a very different predicament, and Batman is suddenly alone facing a boss fight against...
BOSS FIGHT: Solomon Grundy
Solomon Grundy is technically immortal, and his health is regenerated by three power generators on the floor. In the first phase of the boss fight, you need to detonate the generators by quickfiring Explosive Gel (LT+X/L2+Square) onto them and then detonating them when they're open with the same combination. Grundy will fall to the floor and you will need to administer the Beat Down coup-de-grace.
The second phase is the same thing, except this time Solomon Grundy will use his balls-and-chains attacks more frequently. At the end of this phase, a short cutscene with some interactivity will play, which ends with you needing to mash the A/X button to break free from Grundy's grip.
The third phase adds more hazards to the mix. Large maggots will attack you, and Grundy will also send shockwaves that need to be leaped over, in addition to his melee attacks. Once all three generators are destroyed run up to Grundy and Beat him Down to finish the fight.
Now you just need to fight Penguin, who is extremely easy. Run forward and right to dodge his grenade launcher fire, and once you're within melee range, unleash a massive Beat Down to finish him off, triggering a cutscene and ending the dungeon.