I've had to shoot one pitbull while out jogging. I also learned about running with headphones in, as I was unaware of him running up behind me until the instant before he bit me on the forearm. I shot him once in the chest with a PDX-1 .38. He broke off and laid down, but did survive.
A zone partner shot one that had torn up two people and got it in the head with a Federal bonded .40. It rode the skull and lodged under the opposite side ear. The dog broke off but also survived.
Finally, I shot one on duty with a plated 12g buckshot. It was sick and literally foaming at the mouth, animal control requested I shoot it as they could not safely capture it after trying. I shot it through the chest, it fell over and laid there, but then got up and ran under a car. It did not survive, but still took longer to die than I would have thought.
I've had 3 pit bulls over the years, they are fine pets when they are well taken care of. When they go bad, though, they are very difficult to kill.