These guys are easy to tame with a soothing balm. Im a beginner and just started a new game and im in the early 20's of the game. I had completed a pursuit before for killing piranhas, and as a reward i got a sotting balm. I was going to use it to tame a high level raptor, but it didnt work out. But since i heard that these beavers do dams, i wanted to tame one. I went after a 110 level female, and it took about 10 tranqs in the head. I boloed it and shot it in the head. I gave it the soothing balm and then gave it about 30 rockarrots at most. With the soothing balm, i suggest about at least 50 Narcotics. I used about 30, but if it is higher level, i recommend 50 narcotics. Just stay to guard your beaver and itll be fine if you keep its torpor levels up. I honestly dont know how many narcotics it takes to do without soothing balm but i hope this helped! Also, the coordinates of a safe place to find beavers is Lat:n98, Lon: 58.
The method I used to tame was picking up the beaver with my crystal wyvern and dropping it in a taming pen. Pretty easy knockouts but their torpor drop rate is INSANITY and you can't leave then for more than 3 minutes. Feed them either mejoberries or crops (kibble is really expensive but if you want to do that, go for it).