This achievement seems to not work quite as intended, but at least its still easily obtainable. Some players have mentioned that getting all five fedoras doesn't unlock the achievement. But clicking multiple times on a single fedora will unlock it.
Also note that the fedora by the first body doesn't count as one of the five fedoras, for some reason.
Fedora locations
* Gray fedora, "Office": Inside apartment, on a box by the hat hangers.
* Red fedora, "Station": Close by the gas station, go up the stairs to the train station and turn left towards a green glowing information panel. The fedora sits on the bench right next to it.
* White fedora, "Hotel": In Harry Mills' hotel room at the Grand Hotel, on a chest of drawers close to his body and next to the large TV.
* Black fedora, "Docks": On the other side of the gate to the warehouse area, past the guard, but right outside the entrance to the actual warehouse. On a crate.
* Camo fedora, "Lodge": In the hunting lodge, hanging from the top of one of the chairs on the first floor.
The fedoras you've found will be displayed on the hanger in your office, so you can always go there to check on your fedora collecting progress.