You can shoot a beaver all you want with your pellet gun, it AINT GOING TO KILL IT. there skin is thicker then a boars hide then you have all that fat and muscle to get thru. it aint going to happen, you can shoot them with a 22 and they will laugh at you and swim away, shoot them with a 12ga and they do the same thing, your best bet is a #330 trap while in season. their brain is only the size of a pea or smaller an no one is accurate enough to put a pill dead on, on a swimming beaver. I know what I am talking about
I shot one once with #2 Steel out of a 12ga at less then 15 feet to watch it swim away /ubbthreads/images/graemlins/angry-smiley-055.gif /ubbthreads/images/graemlins/smiliesmack.gif. I'll never shoot another one, theres better ways to kill one.
Don't know what state your in, but you better make sure its legal to do before you do it. I know here in Ohio, you have to have a special permit to take a beaver out of season, even if its causing damage, and they don't give out those permits to just anyone, even the ADC guys have to have a beaver permit to do Beaver ADC work. so check before you shoot, would hate to see you get in trouble over a beaver