The game starts right off proving itself a bit harder than the original game. Bear Hugger is not quite as bad as Glass Joe was in Punch-Out!!, but not by much. You cannot do any damage to his gut, so it's useless punching him there. Just dodge and counter or jab at him when he's open and you'll do fine.
After you knock him down, he will do his special move, which looks like a "Bear Hug", when he gets up. He will extend his arms and after a brief pause will clap them together with you in between. If you get hit, you will automatically be knocked down. Use the new duck technique to dodge the attack, then counter with some jabs or hooks to the face.
Bear Hugger is apparently left-handed, since his jabs are usually thrown with his right hand (viewer's left) and hooks are thrown with the left (viewer's right). His hook is very slow, so don't dodge it too soon or you will get hit by it.