The Mystery Watcher appears at the locations below, which correspond to the numbers on the map. If you miss seeing him, you can return at any time to find him standing there - the achievement is not missable. If he is not there, try exiting and reloading the game. During the story, he only shows up in this specific order and you will need to speak with him at one to make him move to the next. Post-game, he will sort of be at all the locations at once and you can do them in any order.
As soon as you leave the Courthouse for the first time, he is on the building across from you.
After leaving the Steel Mill, he can be found at the top of the ferris wheel.
Finishing up at Wonder City and exiting from the Subway you will be told to interrogate someone. During the cutscene the Mystery Watcher can be seen on the building opposite of you.
Revisiting the GCPD for the second time he can be seen, again, on the building opposite from you.
After finding him at the four locations above, your map will open and you will need to enlarge and rotate the symbols to fit the four points you spoke with him at. Doing so will reveal the fifth location, marked with a "5" in the map. Head there to finish the quest (Watcher in the Wings).