I personally wouldn't use a .380 auto. It's a relatively weak caliber (it's significantly weaker than a 9mm Luger). If one aims at the brain stem / medulla oblongata through the mouth and uses hollow point ammo, if their aim is good, it probably would do the trick. But with a larger / more powerful caliber, one has more leeway because, even if their aim is off a bit and the bullet only grazes the brain stem, the shockwave from a more powerful caliber round will be enough to sufficiently destroy the brain stem. So, personally, I would go with at least a 9mm Luger, and if I wanted to err even more on the side of caution, I would go with a .45 auto or even a 10mm auto or .357 magnum. Whatever caliber one chooses, one should make sure to use hollow point ammo.