You get this achievement for the Watcher in the Wings side mission. Basically you just have to track down the Crimson Hooded figure that's apparently stalking you through the city. I've made a map to make finding the locations easier. I also found that going in and selecting the side mission on your map usually helps in getting the "Mystery Figure" to show up.
Also I don't believe you have to do these in any particular order that I found. Except for the 5th one. It only shows up after finding the other 4 Sigil's he leaves behind then you are given a puzzle to solve. Just basically rotate and scale the symbol against the map so that all the Circles match up to where you found the sigils
At some point while your tracking him down location to location,when you spot him from a short distance throw a Remote Batarang at him for the "Catch" achievement.