http://www.youtube.com/watch?v=-27tpWe2mv0&t=5m28s
Right there's the boss. He's really not as hard as he seems, but you can only hit him immediately after he punches at you. You just have to be patient, tap the D-pad quickly, and be quick with the return punch. Basically, stay just out of reach of him as you keep backing up, and as soon as he punches, move up and punch him. Then walk toward him and push him back toward the edge of the screen (not too far, or he'll walk through you to the other side). Keep doing this until he's beaten. It'll take some practice to get it down, but once you do, he's pretty easy.
There's another strategy to beat him, where you just jump kick into him, he squats down and hits you, then you kick/punch him back. You'll do the same amount of damage to him that he does to you, but in the end, you'll win because your character can keep fighting with an empty bar, but the boss can't. The problem with this technique, is that if you miss him once, you're screwed.