"This is the most powerful gun in the world. Nothing is immune to this baby."
Alternately, a scientist makes his monster possible to kill with bullets because a killing machine was not his intention (or because he's worried about his killing machine turning on him).
Discussed: "You know how the monsters in all those disaster movies are always immune to bullets? That's not entirely inaccurate..."
Conversed: "Geez, why do those guys in disaster movies always shoot at the giant monster? It never works!"
The uselessness of bullets leads to an increasing reliance on heavy weaponry by the monster hunters, which in turn breeds monsters who are even tougher, creating an escalating cycle of violence and lots of collateral damage.
Casualties and quitting among law-enforces and soldier skyrocket because their weapons are useless against the monsters, leading to even more depression and fear.
The monster is only one of several antagonists, the rest of whom are not bulletproof, making that monster a special threat.
Another option is that the monster gets stronger, but the heroes are adaptable and intelligent, leading to a Lensman Arms Race.