Either caliber in the head will do the trick, but I'd go with the .22
Aim between the ear and the eye if you can,,,, and like Parks said,,,, expect the "death boogie" cause you're probably gonna get to see it......
I'm having the same problem with squirrels tearing up my new sod lawn. I think they're looking for grubs, which are abundant this time of year and a mighty tasty meal for a squirrel. I also have been on an extermination campaign,,, so far I've gotten only 1 but I'm always on the lookout....
Let us know how you make out, pics would be great too!! :)
Jeff