Why don't you get a goat or pig head and shoot it with the most powerful .22 airgun you can find and let us know.
It will depend on the range, the type of pellet, the part of skull you hit (front is thicker and harder than other parts) and whos skull you shoot.
If you are just shooting a crying baby in the skull, it should be pretty easy. If you are shooting the mother of said baby for letting her baby cry all the time, it would take more power. If you are shooting the baby daddy in the skull because he is trying to kill you for shooting his baby and baby momma, you will need the most power you can find.
"Be master of your petty annoyances and conserve your energies for the big, worthwhile things. It isn't the mountain ahead that wears you out - it's the grain of sand in your shoe."