The Snug in Their Beds Trophy in Batman Arkham Knight: A Matter of Family DLC can be unlocked by solving the puzzles. Batgirl has to find all the puzzles and solve it. Here is the exact location for the 5 puzzles shown below in Maps.
You can do this later after completing the DLC story. The Snug in their Beds uncovers the secret History of the park. To activate the puzzle use your Remote hacking device. The first four can be done in any order you want, but the fifth will be only unlocked after you complete the first four.
Here is the exact Location of all 5 Puzzles in Batman Arkham Knight: A Matter of Family DLC
After Completing all the puzzle, the achievement is done and you are awarded the Snug in Their Beds Trophy.