This is a Side Mission called “Shot in the Dark.” You have to find details for 3 different Shootings, starting with the point of the dead body and bullet hole, followed by tracing the shot back to its' origin for a clue.
First Victim: You meet a political prisoner in the Industrial Zone, which is marked on your map. He is subsequently killed in front of you. Afterwards, trace it back to the southwest to find the bullet shell. After that, you'll be done until you get a prompt for the 2nd victim.
Second Victim: The body is located on a broken piece of highway, northeast of the northern-most Catwoman switch point in the post-game. You’ll trace the shot back through a Water Tower to where a Tripod is. Again, you must wait to find out where his next victim is.
Third Victim: This one is located on the street above where “Park Row” is. Some inmates are crowded around the dead body. After tracing back the shot, and finding Deadshot's outline in the snow, you will be given 3 possible locations to where his stash is. Choose the one on the Northeast part of the map. After that, just follow what needs to be done to complete it and get the Trophy. You will get the Trophy for Forensic Expert after finding his stash.
Thanks goes to Xx Overkill VR over at x360a.org for this photo
Poking around, and it seems that once you have this trophy, if you attempt to go for NG+ to get Perfect Knight 2 this side mission glitches. I am sitting at 98% on NG+ and the Deadshot missions will NOT trigger. :(
this 1 semi-glitched on me.. i had completed the first victim, but by the time i finished the game (story ng+) it hadnt given me the 2nd, i was flying around looking for acts of violence against political prisoners after i finished cat woman's post game mission of taking out two-face, and right when i found an act of violence in the southwest part of the industrial district, the gunshot went off and the 2nd deadshot victim activated..might work that way for others as well