After you have finished interrogating Mayor Quincy Sharp, it is really the time to go back to the GCPD lab and have Freeze develop the cure. Batman doesnt have much time left before he will have to give in to the disease. Head to the G.C.P.D laboratory now.
The GCPD building is guarded by Joker's men. defeat them, and enter the GCPD. Head to the main lab where Mister Freeze is. Talk to him and give him the blood sample. He will create the cure successfully. You will ask him to give you the cure, but he will refuse. The Joker has his wife, Nora. He wants you to bring her back to him. You try to reach for the safe to get the other vial, but he fires at you with his freeze gun. Contact Oracle and tell her Freeze is attacking you, have her get the telemetry feed from his suit. She will advise you not to try and take him up on a straight on fight since he is too powerful.
Your batcomputer will now intercept Mister Freeze's suit telemetry and track the heat signatures. Now starts a BOSS FIGHT.
Don't allow Freeze to see you. He is too dangerous. Use the batcomputer to analyze Mr. Freeze and identify any potential weaknesses. It will process possible attacks:
Structural Weakness: While providing substantial protection, Freeze's suit cannot withstand multiple high velocity impacts simultaneously. Luring Freeze into an exploding structural weakness will immediately immobilize him.
Industrial Electomagnet: Industrial Electromagnets can be powered up using a Remote Electrical Charge, warping and overwhelming any metallic objects within their magnetic field.
Electrification: While Freeze's suit provides protection against most forms of liquid, if that liquid is electrified this will temporarily leave him stunned.
Silent Takedown: Freeze's slow movement and single minded determination to track down his target make him susceptible to close ranged, surprise takedown from behind.
Line Launcher: The Line Launcher gadget allows for rapid attacks from behind or the side to immobilize him. Warning: Once used, Freeze will identify and track the line Launcher's distinctive firing sound therefore rendering repeat attacks impossible.
Glide Kick: Freeze's slow movement speed make him powerless to protect against a surprise glide kick attack from behind.
Ledge Grab: Freeze's restricted field of view leaves him vulnerable to surprise ledge grab attacks.
Reverse Ledge Grab: If lured beneath a raised platform, Freeze is vulnerable to a surprise attack from above.
Floor Grate: The tracking devices use by Freeze do not scan below ground level. An attack from directly underneath freeze would be impossible for him to block.
Use several of those indirect attack tactics against him to bring his defenses offline, and then when your computer says his suit functionality is compromised and his defense are offline and is vulnerable to attack head in and beat him. Then jump out a soon as his systems are reinitialized. You can use each of the tactics no more then ONCE. Here are things you should try:
Use magnet against him. wait until he is near the electromagnet and fire your REC gun at it to attract him to it then head in for the beating. But you can only do this ONCE, as after he realizes what you are doing, he will freeze the electromagnet and you cant do it anymore.
Go up the stairs and wait for him to be underneath for a surprise attack
Use Line Launcher Attacks
Lure Mister Freeze to the exposed wires on the bottom of the room, then press the switch to electrocute him. After that, he will freeze the water so that tactic wont work anymore.
Open the grates and get beneath the floor and use a takedown attack as soon as he is positioned above you.
Perform a few of the above tactics (like four or five of them I Think) and you will have beaten Mister Freeze.