Breather Boss: Godfather Gordon, if you get there with a whip and armor. He has a gun which is probably intimidating normally, but it can't hurt you if you're armored, and you can slap him with impunity if you've maintained a whip. He goes down pretty easily.
That One Boss: Gordon's body guards. By far the hardest obstacle to seeing the ending. You know, unless you have a whip. Other than that, the first Beat 'Em Up boss is a hassle because his range seems to slightly exceed yours and the best weapon you're taking to him is a stick. Nobody on the way uses a gun, let alone a whip.