In the previous chapter, you cleared the GCPD building and learned that Mister Freeze is being held hostage by the Penguin in the Gotham City Museum. You need to find the cure to Joker's disease in order to save yourself and the residents of Gotham from imminent death, and it appears only Mister Freeze holds the key to the cure.
The Museum should now appear on your map. Set it as your destination and make your way towards it.
There will be guards around the museum. You can choose whether to fight them or slip by them. Head towards the Museum Main Entrance. You will have to dispose of the thugs there.
Use the Cryptographic sequencer to hack the museum door. The password will be "Fossil". Enter the front door.
There will be some of Penguin's fog in the corridor where you enter. They will be armed with knives. Take care of them.
There are 2 windows you can smash through to access some side rooms. One of the siderooms will have some Riddler Trophy. The other will have a security terminal which you will want to hack using the cryptographic sequencer.
Use the sequencer to hack he security door. Suddenly while attempting to hack the door, you will hear Penguin:
"I don't think I want you breaking into my little home, Batman."
You realize that something's blocking communication back to the Batcave. Penguin must be using military grade communication disruptors. The only way to crack this security is to destroy them.
Scan the Jammer Signal Direction. Your new objective will be to disable Penguin's Communications disruptors. Use the Disruptor signal tracker to track down the disruptors. They are outside the museum.
The first transmitter will be on the roof of the museum, towards the Northeastern side. There will several guard guarding that disruptor. Take them all out. After that, disable the communications disruptor.
The jamming tower has 3 terminals attached. You will have to destroy all three to shut it down. Destroy all the terminals.
Now it's time to destroy the next jammer. Use the disruptor signal tracker to locate the other disruptor which will be around 100m from the first one on the top of some roof. It will also be guarded by 2 people, one of them armed. Defeat them and get rid of the jammer. But even after having destroyed the two jammers, the signal's blocked again. Sounds like Penguin's final jammer was activated underneath Arkham City.
Your new objective will be to disable Penguin's final communications disruptor underground. Follow the waypoint marker to the subway station. Enter the station and climb down the stairs. Defeat the henchmen inside. Find the tracks. Follow the train tracks and reach an old train. climb it. Keep going past a hallway that has a TITAN container. You will reach a big room with a painting in the end and some thugs. Knock them out and keep moving. Use Batman's REC electronic gun top open the door. Go through the vent and attack the thugs in the big room on the other side.
Disable the final communications disruptor.