You can watch this video or read my guide.
Credit: Batman Arkham Videos
If you see the calendar man or the political prisoners, you don't need to go to them.
On the cutscene with you receiving information about what Protocol 10 might be, Catwoman nearly gets shot in the head by a bullet. After the cutscene, you are required to find out where the bullet came from. Once you find out, you need to follow the line in detective mode. This should lead you to the Medical Center. Take out the goons at the front and afterward enter the building. Once in, you will be attacked by Harley, remember to counter her. As soon as she leaves, you will be allowed to drop a smoke pellet (may have gotten it wrong). This allows you to grapple up, out of sight, and take down the armed thugs, the game explains how to do this. Once you take them out, the steam achievement is yours forever