Thanks to those that caught my errors in the comments and helped me make this better.
Early in the chapter you will go to the police station to meet Dee for lunch. There is a note on the wall to the left of the kitchen. Read that to mention “kid sized”. Go upstairs to drop off your file next to Eddy’s door.
When you are ready head to the kitchen and choose the cobbler. Pay attention to Dee outside and when a woman comes in to talk to her choose to “eavesdrop” to find out the Mailbox Bandit is an animal/raccoon. After that you can just wait or talk to Greggs. Dee will come in and mention catching the Mailbox Bandit. Hold LT and from the options, choose “it was an animal”. Achievement should pop shortly after she confirms.
If you miss the LT event or don’t get the “animal” option, you will have to retry the achievement through chapter select.