You will be informed of the possibility to approach this mission as you're travelling through Arkham City, a prompt saying that a ringing phone has been detected in the area will appear #1. Land on the ground and use the Detective Mode to locate the phone #2. The conversation will unveil that it's Zsasz, known from the previous game. He will force you to participate in his crazy game in order to save innocent people.
Initially you won't be able to do anything, so wait until you receive another information about a ringing phone. Just like before, you have to land and pick up the phone #1, though this time you will receive the real challenge. You will have to reach another phone booth in a different part of town #2.
The main difficulty is of course the time limit #1. I'd suggest planning a route on the map (you might have to avoid the restricted area). The Grapnel Boost gained for completing the AR Training would definitely come in handy here, as it's able to catapult Batman. After reaching the destination, approach the ringing phone #2.
It's not the end though, as now you will have to manually locate the spot from Zsasz was calling. In order to do that, use the left analog stick to follow the area showed by the game #1. Try not to lose the signal for too long and keep it up until the conversation ends #2.
The further part of this quest will have a very similar course. You will be able to pick up new calls from time to time #1, each time having to reach a new phone booth in the time limit #2. It will let you resume the search for Zsasz.
You will have to repeat this until you fill up the green bar at the bottom of the screen #1, thanks to which you will be able to locate Zsasz. His hideout is in the Industrial District #2 and that's where you need to head.
After reaching the spot, you will have to eliminate a couple inmates #1, though you shouldn't have problems with it. Afterwards find the interactive door #2 leading to Zsasz's hideout.
Go down the stairs. Don't bother with trying to open the door here, as it's locked. Instead turn right, take out the Batclaw and use it to pull out the ventilation shaft grate #1. Afterwards use the Grapnel Gun to access the shaft and head to the room where Zsasz is holding two hostages #2.
Theoretically it could seem that Batman should avoid Zsasz's sight, but he will probably be so occupied with his hostages that it won't be really necessary. Get out of the shaft #1 and head forward. Stop by the ledge and wait a couple seconds to note, that the water level keeps changing. Wait for it to come up and cross the bridge #2.
Pass the room where Zsasz is and stop after reaching the end of the current ledge #1. Here, you can act in two different ways. The first method is jumping to the ledge in the distance #2, though you would have to do it when the water level goes down.
If you don't want to risk, you can use the Freeze Blast and create an ice float with it #1. Jump onto it and use the Grapnel Gun #2 or wait for the water level to raise.
Regardless of the chosen method, after reaching the new ledge you need to head left. Start running here #1 and afterwards perform a slide (right trigger). If you have done everything correctly, Batman should automatically grab onto the ledge #2.
Move right until you reach a new ledge onto which you can climb #1. Go left, stopping after reaching another gap #2.
Don't use the Freeze Blast, as the drill would destroy the ice anyway. Instead, wait for the water level to raise and jump towards the new ledge #1. Make a few steps forward and only afterwards use the Freeze Blast to create an ice raft #2.
Jump onto the ice, wait for the water level to go up and use the Grapnel Gun to grab the grapple point above the last platforms #1. Pull yourself towards the new ledge and jump onto it. Crouch and carefully go left. Wait for Zsasz to stand by the glass wall #2, approach him and press Y.
If you have done everything correctly, Batman should attack Zsasz by surprise #1 and take him down. You can talk with the political prisoners, though it's not necessary. In order to get out of the room, use the previously inaccessible door #2.