When you first get the cursed fedora at the beginning of Chapter 1, immediately head to the Boardwalk. (If you haven't been there yet, there are a few ways to find it. One is automatic, and you can also just wander) Go to the guy that pays Meat for pictures with different hats there at the Boardwalk, and have him take one with you wearing the cursed version of the hat.
Then just head back to the antique store, remove the curse from the fedora, and head back to the boardwalk. Take another picture with the uncursed fedora, and the achievement is yours.