I found a level 16 for my pursuit to tame one. 2 Galli kibble and 10 (probably overkill) did the trick, took 2-3 minutes. 2-3 tranq darts will knock it out easily, just wait a second or two inbetween shots. Best wood gatherer, do not listen to anyone else. Also I've heard it can be a mobile smithy.
Quite possibly the most useful animals in the game imo. It is much more than a wood gatherer. It is a mobile smithy. Anything you can do on your smithy at the base you can do on your beaver. Repair tools, craft behemoth gates, etc etc.