There have been a number of Cougar attacks on humans in recent years, but the Cougar doesn't normally hunt humans so a man killer is likely to act in an atypical manner.
They seem to have a taste for hikers and cyclists, though they may just as easily show up in your backyard in broad daylight.
Best way to drop a hyped up predator is to cut his spinal cord.
Brain shots are fine, but the skull structure of predators can be misleading, and coupled with difficulty in hitting a moving target you can put a bullet through the eye yet miss the brain case entirely.
This is especially so when it comes to Black Bear. The brain of the Blackie sits far lower in the head than that of any other breed of bear. The brain case is narrow and theres nothing much behind the eye socket other than soft tissue. A straight through shot to the eye won't touch the brain case.
Since bears commonly wallop the heck out of each other with blows that can break a steer's back, impact on soft tissue alone may not even stun an enraged Blackie.
A 500+lb Blackie killed a young girl not far from here several years back. during the attack a female officer emptied her .380 off duty piece into its back and head with no effect.
Large predators often have teeth stout enough to deflect a light rifle or pistol bullet.
Smaller Blackies may be dropped with a .32 S&W in the right place. The grandfather of a friend used to walk right up to them and trick them into standing, then plug them once in the pump with his .32 hand ejector.