You got to remember, Beaver are nothing but overgrown rats. They are stupid. When you see them splash and dive, just go and sit down nearby. Soon they will surface and start swimming right out in front of you if you are still, and a little hidden. As they swim by with only their heads out of the water makes for a perfect shot. Or they will climb out onto shore and give you a good chance to make a stalk and a head shot as they chew on a tree. Body shots, heart lung area, are to be avoided if possible. Reason is they will head for the water fast, and if it is flowing water, and they reach it, you will never see them again. That is one time I like the .17HMR, a body shot and I can usually reach them before they make it to the water. It slows them down more than anything else I have used, without going all the way through.
I'm always laughing at my partner. He uses a .22 Mag. Good with head shots, but body shots and they head for the river. Got to say that old man is fast on his feet. He heads them off and thumps them in the head with an Ax. Then complains about the two holes in the pelt, and the tear in the head area from the ax. Still insist on carrying that .22 Mag, but has been caught using my .17 HMR as of late.