It took 8-9 shots to take him out... The .177 pellets didn’t seem to do anything to him so the last shot was with a .22
I'm putting this in a spoiler, so people can skip it.Headshot, and close.
Body shots with a .22 aren't going to be enough. Larger caliber is better, but a .22 is enough IF the placement is correct. You want to hit the brainstem if at all possible. Back of the neck, angled to point about at the animal's mouth. OR, into the mouth, pointing toward the back of the head. Into the ear can work too. A .22 can do a lot of damage to the brain, because it usually ricochets around inside the skull.