What do you recommend...a slingshot? Almost any center fire cartridge of 357 bore or larger with a very hard, non-expanding, flat nosed bullet will pierce a bears skull with direct /frontal (between the eyes) hits. From the side angle, a shot right at the bottom of the ear canal is instant death. These two shots will guarantee a dead bear, if you are using the correct ammo. The old MYTH that bullets will slide off a bears skull is pure hogwash, when using modern ammo featuring bullets that will not mushroom when fired out of a powerful handgun.