***UPDATE 16th of February 2020***
"Kooky Cow 32" reports, tha the unlocked the achievement as a second players, so this achievement may be fixed. I can't confirm this and would still recommend doing this as described below.
Original Solution: A quick heads up for everybody. As of now (15th Sep. 2019) the tracking for this achievement only works when you are the host or you are in your own singleplayer game.
DONT UNLOCK Skins/Heads from your inventory or buy them from Earl when you are in the game of another player.
When you find Heads/Skins, keep them, start your own game and unlock them.
EDIT: If you seem do not find any more Skins/Heads, the 3rd Slot-machine in Moxxis-Bar has them as rewards. Also: Playing another Character and finding the heads for the other classes is an option.
Clarification: The third slot-machine is the third one from the entrance. The first right around the corner. Check the boards directly above the 3 slot rolls, the prizes are displayed there. The third one will have have multiple heads as prizes.