Take the Northern exit from the arena and walk up the stairs. Ignore the map's indications, because you can reach the Penguin's office by taking a shorter way. Go towards the Eastern hatch that will take you to the Deck Access Corridor. After you get to a part which you have not explored yet, jump down where there is a destroyed ladder. Then walk ahead.
Run up and jump over the hole in the floor, and then slide, which will allow you to get around another obstacle. After you reach the corridor's final part, jump up to reach the ledge above and walk through the shaft. Take one more slide and wait for Batman to land safely in a new area. Stop at the wall on the right, select the explosive gel from the inventory and spread it. Detonate the gel, which will unlock further passage for you.
Approach the edge and use the hook to reach the balcony above. Do that again with the next ledge and start running. Then jump to reach the ledge in front of Batman. Turn left here and take another leap, after you run up, this time to reach the interactive orange ledge that you can see in the distance.
After you have reached the final part of the ledge, look up and use the hook again. Turn around and aim at the highest-located balcony, thanks to which you will end up next to two guards that talk to each other. Throw one of them over the balustrade and deal personally with the other one., who will pose no serious threat to you anymore. You can now go towards the hatch to the ship's Upper Deck.
Around the corner, you should notice three enemies and this provides you with a rare opportunity to launch a surprise-attack. I recommend that you use the remote control batarang here, to knock the armed enemy down, or spread the explosive gel in the area (it is especially recommended if you have purchased an upgrade for the gadget which equips it with proximity detonator). Regardless of what action you have taken, deal first with the guard, and take to his colleagues afterwards. you can now walk though the nearby gate and ignore the discharges that you can see above it.
After you reach the final part of the corridor, turn left and unlock access to the venting shaft Enter the tunnel and pry the next grate after you reach its end. Soon, you will reach the restaurant and you may go towards the door to the Casino straight away. It is necessary that you crouch here because there are three enemies around and it would be a good thing if you eliminate all of them by surprise. First of all, focus on the enemy with the gun, and try to reach him without getting detected. (make use of the nearby columns in the form of cover). Perform a silent takedown on this one.
You may now approach the remaining enemies. What is interesting, you do not need to choose which one you want to attack in the first place because, if you stop precisely between them, pressing the silent takedown key/button will cause eliminating both of them simultaneously (the above screenshot). Wait for Batman to obtain another SIM Card and watch a short cutscene featuring Tracey.
Get ready to fight another battle. Just like in the case of the previous fights, set appropriate priorities for yourself. First of all, eliminate the enemies equipped with knives and firearms. Also, avoid the heavy objects that the enemies throw at Batman (or destroy them with batarang). Finally, take to the armored enemies by stunning them with the cape and initiating a fast combo.
Wait for Batman to decipher Penguin's another transmission and locate entrance to the venting shaft in one of the casino's corners. Walk through a short tunnel here and after you get to a small room, select the Cryptographic Sequencer. Use the sequencer on the control panel to break into the system and determine the password (the screenshot).
return to the casino and deal with the enemies that you find there. It is worthwhile to act quickly here, and consider using additional gadgets, because two of the bandits use firearms and they pose, as a result, quite a big threat. After you win the fight, go to the room where the enemies that you have just eliminated, used to stay and press the red elevator button.
Take the elevator to reach Tracey's office, and be prepared to press the counter-attack key/button when the moment is right. You need to use the Cryptographic Sequencer once again, this time to hack into the computer that Tracey used to work at. Solve the hacking mini-game by determining the correct password (the screenshot)
[New Character Trophy: Tracey]
[New Character Profile: Candy]
Approach the big glass fragment of the wall, run up and smash through to the other side, to land in the casino's main area again. Try to open the southern door, which will result in another fight with another group of bandits commanded by an elite enforcer. First, deal with the regular enemies and perform numerous dodges to avoid the elite bandit's charges. Focus on eliminating this one as the very last, by stunning him with your cape and landing a series of quick attacks (the screenshot). You can now take the Southern door. Walk through the Foyer, to walk into the Theater.
[New Character Trophy: Penguin's Enforcer]