He's easier than Piston Hondo, but don't underestimate him. He's quicker than his size would lead you to believe. There's not one single dodge that'll evade all of his attacks, though generally you're safe dodging to the left unless you know that his Bear Hug punch is incoming. When you dodge one of his two lesser punches, follow up by attacking to the head. If you try to tag Bear in the body after dodging his two regular punches, he'll block the blows. After dodging his Bear Hug double-arm punch, you can hit him however you choose.
Try to keep at least one star punch in reserve to catch Bear any time he taunts you with his hands up. Hit him with a star punch during this taunt and you'll get an instant knockdown. His taunt is Bear Hugger making a face. Wait for Bear to flash yellow and then quickly tag him in the face with a jab (either left or right) to earn a star. You can hit him in the gut, but it won't give you a star. If you already have a star, you can tag Bear during this taunt for an instant knockdown, but the timing is pretty strict. You have to trigger the star punch immediately as he begins the taunt, or he'll finish up before your punch is unloaded. The other taunt is when Bear will occasionally step back and spin his hips around, jiggling his belly back and forth. If you try to throw a punch to his head, you'll whiff. If you try to throw a star punch, you'll whiff. And even if you try to throw a hook, you have to time it correctly to make it hit. Wait for Bear Hugger to roll his belly toward you and tag it with a hook to earn a star.