Circumstances of unlocking the case: This case may become available while you are exploring the game world freely, around The Amusement Mile district (there will appear an appropriate piece of information on the screen, and a new entry in Batman's journal).
You start this investigation in the crime scene shown in the above screenshot., which is located in the Southern part of The Amusement Mile district. After you get there, listen to Batman's commentary and turn on the evidence scanner.
Start by scanning the man's corpse to determine, as a result, that he was a reporter. Repeat the scanning, thanks to which you will watch the preliminary version of the events.
Now, scan the DNA trace located right next to the edge, which will allow you to expand the current reconstruction by a new piece of information.
Finally, towards the end of the examination process, you will have to follow the red line that shows the trajectory of the photo camera that belonged to the journalist. To do that, use the appropriate keys/triggers, which will manipulate the reconstruction playing process. The device that you are looking for is lying on the ground, close to the corpse (the above screenshot) and you need to scan it to determine the murderer's personals.
This is not the end yet, because you need to arrest Chucky Berks, i.e. the man responsible for committing the murder. He is staying on the rooftop of one of the buildings in the Diamond District in the South-Eastern part of the city. Since Chucky is surrounded by a few goons, it would be a good idea to attack them by surprise to eliminate one of the bandits right at the outset.
After the fight proper starts, start attacking all of the enemies, including Berks. Eliminating all of them will not be too demanding, fortunately. Leave the murderer for the end, because there will appear the option to interrogate him after you have weakened him sufficiently (pressing the key/button displayed on the screen). Chucky will admit to have committed the crime and the investigation will be over.