Can a air rifle kill a boar?

Yes I killed one yesterday with an air rifle it took 3 shots to the head but yes it can be done.

Yes there are air rifles that are capable of killing Boars. The usually are in the class of PCP (PreCharged Pneumatic) air rifles. They come in the larger calibers beyond 22 caliber, you will find them in .9mm, 45 Cal and 50 Cal pellets. They require a special hand pump or a Scuba tank to charge them to 3000 Psi and will bring down a Boar or deer.