First meeting with the Stalker
You will gain the chance to approach this mission while exploring Arkham City. On one of the roofs in The Bowery #1 you should meet the Mystery Stalker #2. Approach and speak with him.
Take a look around the place where he was and you should find a painted symbol #1. In accordance with the received information, press LB to scan it #2 and note the marks that will appear on the map.
Second meeting with the Stalker
The second rendezvous with the Mystery Stalker will take place on one of the roofs in Park Row #1 #2. Just like before, you will have to scan (LB) the symbols he leaves behind.
Third meeting with the Stalker
The third meeting with the Mystery Stalker will take place in the Amusement Mile district, west of the GCPD Building #1 #2. Just like before, locate and scan the symbol.
Fourth meeting with the Stalker
For the fourth meeting, head to the eastern part of the Industrial District and find the Ferris Wheel #1 #2.
Use the Grapnel Gun to reach the highest passenger cars and on one of them you will find the Mystery Stalker #1. Listen out to what he has to say, jump onto the next roof and scan the symbol #2.
Fifth meeting with the Stalker
Now you will have to complete a bit harder puzzle to locate the place of the final, fifth meeting. Wait for the Arkham City map to open and note that you can use both analog sticks to manipulate the unlocked symbols. The left is used for moving and the right for rotating and enlarging, from which I'd recommend to begin. Afterwards turn them around and try to place them on the four previous Stalker rendezvous points. The solution can be seen on the screen above.
As you have probably noticed, solving the puzzle will cause a new points to appear on the map #1. It's located nearby the Church, where you have to head now. After getting there, land on the small cemetery at the back of the building #2.
Examine every wall of the church and on one of them you will find painted symbols #1. Scan them just like before, by pressing LB. You will speak with the Mystery Stalker - Azrael #2 - for the last time and therefore end the mission.