In the credits of the game, Bear Hugger tells you that it's possible to defeat him in less than 17 seconds. Pulling it off it is much harder than you'd think it is. The key is to get no less than 5 punches in when you counter his first attack, then quickly hook him in the stomach at the earliest possibility. This is by no means the fastest, as I can never get him down on the first KD, only on the 2nd.