Big Fat Mutants are an evolution of the Muscled Mutant. With its very high health and high damage, it serves as a meatshield that can punch out just as much as it can take, in addition to being able to inflict bleeding or fractures.
The big fat mutant will move toward the player at a slow speed, lunging when it gets close like a normal mutant with a comparable distance. Its attacks are more deadly, and it has a significant chance to fracture bones or cause bleeding because of its attacks.
It has two distinct attacks. One is a simple straight hook using one of its fists; the other is a straightforward thrust with both of its fists. It will lunge a respectable distance (about the distance of a shotgun shot) during its punch, so being anywhere near melee range can hurt. Both attacks also have a distinct wind-up animation.
Shielding while anywhere near it is recommended, if not to mitigate the damage then to avoid the fractures or bleeding that may accompany it.
Due to its size, hitting it with an SMG is relatively easier compared to other mutants, so using an SMG can easily take it out while staying a safe distance away from its fists. Weakening it with a grenade or plasma launcher shot before attacking it can help; then you can go in and finish it off with a melee weapon or shotgun. Due to its damage potential, though, the safest option is to attack it from a distance with a pistol. With a few critical hits, even a basic pistol can kill a big fat mutant before overheating.
Like all melee attacks, each of their attacks has a noticeable cooldown, so an experienced player may opt to use a shotgun between their strikes. Three or four basic shotgun blasts will kill it on Nightmare.
Big fat mutants have the highest health of all enemies, so they can quickly deplete resources. You can expect them to begin spawning at around 40% local infection, and to increase in numbers from there. For extended trips, the best strategy is simply to keep the infection down so that you can avoid them altogether.