A few decades back in the Smokies, a guy killed a charging black bear by sending a .22lr rifle round through the brain stem when the bear reared up and opened its mouth to snarl. The bullet went through the back of the soft tissue throat and into the brain stem, dropping the bear instantly. Of course the shot was a lucky one because the guy was just aiming to try and hit the bear in the head and hope that discouraged the charge; the open mouth removed obstacles to the back of the throat and the brain stem.
A .22lr can be very effective, but at my current age, I've moved up to a 9x18 or a 40cal, for more impact and more ammo at hand.