In the future or for any other posters to maybe reading this and can not use a firearm. I recommend .22 LR CCI subsonic. If you can't use that use a break barrel pellet gun or pcp pellet gun. Preferably .22 but .177 would work.
Pellet or BB
might do the trick, but
only if you hit it in the eye
and the pellet or BB made it into the brain.
The .22 sub sonic would have to be a head shot as well. Badgers are tough, and know no fear from larger animals.
GRIZZLY AND BROWN/KODIAC BEARS don't mess with them, given a choice in the matter. Badgers are known to steal the bear's kill while the bear is there, and before it has finished eating! They chase the bear off! (Puma's, too. Honey Badgers steal African Lion's kill.)
A body shot with a .22 isn't going to drop it, and is more than likely to just piss it off. A body shot with a pellet or BB? It probably won't notice.
If you can't use a firearm (.223 with hollow point expanding bullets would be my minimum recommendation, if not a .44-40/.45LC/.44 Russian/to .44 magnum for a big hole, or a .30-30) then a 40+ pound draw bow, and a
sharp fixed (not expanding) 2 or 3 blade broadhead into the "boiler room" will do the trick.t
might be a good idea to give him/her/it the arrow from a tree stand, or from the chicken coop roof, behind the chicken coop fence, so it can't reach you "if" it decides to attack (like there'd be any other alternative from its point of view) after it gets the arrow.
An arrow through the lungs and heart
will kill it. However, it may take a minute or three for the badger to realize it has been turned off, and it
will be in a rage until it is off.