Here is a tip for guys using little bullets. Sight your gun in at as close to the range as you usually shoot 'em - then shorten and extend your target so you know exactly where your bullets hit at each distance. Of course we usually hit the water when a beaver is swimming, so figure out the ranges so this does not happen.
The next tip is a tough one to follow - but worth it. Shoot 'em in the lip. Not kidding - try it. The beaver will climb out and die on land. It seems that he cannot hold his breath, and there is a major blood vessel in the lip/tongue area and it is at least five times more likely to get your beaver than a head shot. Even a little bullet is enough.