Without Nunchucks - If you crouch and wait for him to come to you, you will never be able to hit him. Walk straight up to him. Harly Hog will start throwing punches. Get close enough so that one punch hits you. Then crouch and punch continuously. At first your punches may not hit, but he will start moving backward, and once he is at a certain distance, you will be able to punch him continuously without getting hit once. Once you have hit him, do not stop punching.
Without Nunchucks - Walk as far to the right as you can (up to the back of the van). Mad Dog will jump over you. Crouch and punch continuously. There is a bug here that will allow your punches to connect even if he is halfway across the screen. Mad Dog will walk back and forth and occasionally lunge at you. When he jumps toward you, he will hit you, but then he will back away. Keep punching. He will eventually fall over.
Macehead the Horrible
He swings a mace around over his head. If you try to avoid it, he will undoubtedly hit you with it. When you attack him, he will drop the mace. Even though you will get hit, it will be to your advantage to attack him as quickly as possible. (Walk straight up to him, crouch and punch or use the nunchucks.)
Without Nunchucks - Crouch and wait for him to come to you. Right before he gets to you, punch and immediately back away or he will kick. When he starts backing away, walk toward him, but don't get too close or he will kick. After a few steps, stop and wait again. When he gets close, punch again. You will probably have to try this several times before you get the timing right. You want to hit him right as he stops moving, however, if you wait for him to stop and then punch, you will probably not be quick enough--he will kick you first. Also, sometimes you can get in more than one punch before he kicks. It is tempting to try this, but the only safe bet is to punch once and get out of the way.
You will find him standing on a platform above you throwing dynamite down onto the ground. Even if you walk into a dissipating explosion, you will still take damage. Two or three jump-kicks will knock him off the platform.
With Nunchucks - Crouch and wait for him to come to you. Right before he gets to you, use the nunchucks once. He will stagger back and come at you again. Use the nunchucks again. As with Macehead, you will need to learn the proper timing. You want to hit him right as he stops moving, but before he has the chance to attack.
Without Nunchucks - Attack him in the same way as described above for attacking Macehead without nunchucks.
With Nunchucks - You will definately need nunchucks to defeat Giant Defiant. If you lose them in the course of the round, you can go back and get them, but first, fight your way to the end of the I-beam you're walking on. Once you come to the end, you can walk all the way back to the beginning of the round (to get the nunchucks) and no enemies will appear. If you start walking back before you reach the end of the I-beam, you will still have to deal with the common thugs.
Once you have the nunchucks and you have jumped over to the second I-beam, approach Giant Defiant. You should be able to beat this boss without ever getting hit, but just in case, move towards him a little so that in case you get hit, you will not be knocked back off the edge of the beam. Crouch and wait for him to come to you. Right before he stops moving, (you will have to learn the timing,) hit him once the nunchucks. He will jump back and start walking toward you again. Continue using the nunchucks in this manner until he falls over. If he kicks you, be sure you keep a safe distance from the edge of the beam.
Chokehold - In round 1, there are not many common thugs to deal with, so it is safe to attack these enemies. Starting in round 2, you will often be attacked by two or more common thugs at the same time. When this happens, it is safest to simply jump over any of these guys. If one starts choking you, wiggle the D-button back and forth (left and right).
Rogue Rider - They appear at the beginning of round 3. You can knock them off their motorcycles by using the nunchucks, or by landing on them with a jump-kick. Getting run over hurts you. Standing in a cloud of exhaust hurts you. Walking through a motorcycle explosion hurts you. Rather than fighting Rogue Riders, you should keep walking to the right, jumping over the motorcycles when necessary, just to get out of the area as quickly as possible.
Hitman Harry - In rounds 3 and 4, you will find a Hitman Harry laying on the ground shooting. Walk up to him, jumping over his shots. When you get close, he will stand up. You will also come across a standing Hitman Harry in round 2, and in round 5. When a standing Hitman Harry shoots, be sure to duck. (While ducking, attack any other enemies that are coming at you.) Walk a few steps towards him and duck again before he shoots. Keep walking and ducking until you get to him. When you're close enough, duck and punch him in the legs.
Mo-Punk, Dirty Jack, Club Thug and Wild Wacko - No special strategy is needed to beat these guys. However, note that when they're coming up behind you, you can often outrun them and so avoid being attacked (or at least avoid being attacked by more than one enemy).