Brains of mammals, while larger or smaller, are constructed in similar fashion.
Assuming that you can get to it, note on all mammals where the back of the skull opens, and the top of the neck begins.
At about a 45 degree angle upward, a shot directed in that area will destroy the pons--the nerve center of the body. This is the body's circuit breaker--destroy it and death is instant.
As for the firearm used to put the animal down, a .40 caliber bullet or larger will usually do the job for medium sized animals. This is assuming that you can approach the animal from the rear and deliver the shot from almost muzzle contact range.
Hiding in plain sight...