Unlike the worn fedora, the battered fedora is one of relatively few hats that can be upgraded with high defensive stats using the ballistic weave upgrades. The fedora is made of a dark felt and has a black sweatband. Unlike the worn version, the battered fedora lacks a curved brim. It matches the farmhand clothes.
One may be found in Monsignor Plaza, on the shelves behind the counter in the clothing store.
One may be found on the roof of Faneuil Hall, on a table.
One can be found in Haymarket Mall. Go up the stairs that appear when entering, and go into the first room (it has mannequins and collapsed shelves). It will be on one of the shelves that is still standing.