Locate Nora Fries
You will receive this mission after defeating Mr. Freeze, during Defeat Mr. Freeze #1. Start off by heading out of the GCPD building #2.
Open the map and you should note that in order to find Nora Fries - Mr. Freeze's wife - you need to head to the Industrial District (south-east part of Arkham City) #1. To be precise, you have to land on the platform drifting north of the island on which the Industrial District is #2.
Turn to the south-east and you should note a destructible wall #1. There's water separating you from it, so equip the Freeze Blast and shoot at the water to create an ice raft #2.
Jump onto it and prepare the Batclaw. Aim it at the grapple point above the wall and start pulling yourself in #1. After reaching the wall, choose the Explosive Gel, spray #2 and detonate it, unlocking access to a new location.
Once again aim at the grapple point #1 and reach the ledge behind the wall you have just destroyed. Open the door leading to Storage Warehouse 5B #2.
After getting inside, search for a ventilation shaft entrance #1 and use the Grapnel Gun to get inside. Eventually you should reach a room with a big group of enemies inside #2.
Of course it's a good idea to start the fight with a surprise attack, activated by pressing Y (you need to be nearby one of the inmates) #1. The fight itself will however be quite hard. I'd especially suggest keeping an eye on the weapons locker, stopping enemies from opening it as long as possible #2. If someone manages to take out a weapon, you should focus your attention on them in the first place.
Apart from the armed bandits, you should also look out for the ones equipped with blades #1. I'd also suggest dodging often, as some enemies will be throwing various items at you #2.
In the end take care of the shielded enemies (B, A, A) #1 and the armoured one (B followed by tapping X) #2.
Once the battle is over, Batman will automatically note Nora Fries frozen body, no need to interact with it. You can return following the same path or go through the main door #1. In such situation, you would need to hack into the nearby control panel using the Cryptographic Sequencer and create a password #2.
Return to Mr. Freeze
In accordance with the received information, you will now have to return to the GCPD building. don't try using the main entrance, because - as you probably remember - it's frozen. Instead, try reaching the backdoor by gliding #1 and with the help of the Batclaw. Enter the building #2.
Head to the main room of the GCPD building (you will have to once again neutralize the steam with the Freeze Blast) and speak with Mr. Freeze #1 to inform him of the state of his wife #2. He will thank you and the mission will end.