Hmm how big is .22 ?? is that .22 inch, or 5.5mm ??
I have a 4.5mm Weihrauch air rifle, and it takes a hit into the eyeball to take down a cat from the heating pipes in the pig barn... A wildered cat in our barn ate the ears, tail and nose of newborn piglets, right after birth, directly behind the sow.
Off course this cat had to go, but i couldnt capture it. After taking a direct hit between the eyes, it shook its head and crawled between the roofplates and insulation panels. When it came back sitting on those heater pipes it was glaring at me, so i shot it right in its left eye, so its said meoww.. while dropping on the ground: Then i took my hammer and gave it the final blow... Only very lightly, because i was afraid to get brains all over me.
I jumped a foot or two in the air when it turned its head at me and ran away suddenly: then i finally cured the problem by taking a 3 feet long, 2x3" solid steel tractor drawbar and dropped that on its head (at safe distance to not get covered in brains)
It effectively flattened the skull, but lucklily it wasnt very messy.
I hate killing animals, but after putting down several piglets whose ears, tail and nose were chewed off, this mutineer had to go, and i did what had to be done...