I recommend normal for this one, it's not that hard. Average difficulty with bare fists, the way I did it. Very easy with the double gauntlet. Things to do:
1) Don't use spears or bombs, you only need to use your fists. According to Chaos Mythology the gauntlet (beat the game on normal to unlock it) does not void the achievement (ignore the missleading picture) and the double gauntlet (beat the game on Joe Must die) is the easiest way to get this achievement.
2.1) Avoid the gators by sticking to the wall or bait them to chase you and then get out of the water. Most of them despawn for a while after you have reached the ground.
2.2) Or if you are quick enough and you have the single or the double gauntlet, you can punch them in the face and kill them, according to the people who commented.
3) Swamp Man boss fights are not hard. Just use your combo.
4) Go all in when you see a Fat Molded. Combos will interrupt their vomiting attack.
5) Go stealthy and use stealth kills when possible. Helps a lot.
6) Four leg molded: That is the only danger. Try to bait them in a corner, then crouch and punch. Sometimes you will hit air but keep trying, 7-8 punches and they are down.
7) Only on normal on this one. Joe must Die is really hard plus you need to use throwing knives which will maybe void the achievement.
That's all I suppose. If I forgot something comment below. If you downvote, provide the reason. It really helps and its an expression of maturity. Thank you.