Make sure no other Castoroides are around then bola it and shoot it with tranqs until it knocks out. Make sure you bring loads of bio toxin, because their torpor drains fast. I used this method and tamed one at level 42
The way to tame these guys is to run up to one of their dams and then open it and then immediately close it (you don’t have to take anything from it, opening the dam will immediately aggravate all and any nearby beavers). Once this step has been done, you must bola the beaver (assuming only one tries to fight). I actually made a hearty mistake and bolaed the first one that came whereas I should’ve killed the second first (I was making a video, the second one got killed). Once the beaver is bolaed and separated from its mates, go behind it where it can’t hit you and hit it with a bat until you knock it out, but before doing any of these either kill jellyfish for bio-toxin for torpor (the beaver’s torpor will drain quickly) or farm a bunch of narcoberries in preparation. These guys are herbivores so you should also farm other berries besides narcoberries, or gather from the nearby forests. Keep in mind that beavers EXTREMELY slow eaters when knocked out, so patience is your weapon here.
Always use kibble! I tamed a level 150 with pure mejoberries... Had some carrots too, it was an entire afternoon of checking it's torpor. It's nice and all but it doesn't have too good weight. I would get 1000-2000 wood and go back to base fairly unsatisfied. I use mammoths now since they can defend themselves, gather berries as well and hold a TON of wood. I'd rather collect less but hold more than collect more and hold lesd since that just means less trips back to base and a more fullfilling trip each time.