To play as the Wrestler, and thus unlocking this achievement, you'll need to clear the entirety of the Slums using nothing but your fists. So, no weapons of any kind can be used; just your fists.
This may seem a little daunting at first, but it's really not that difficult as the missions in the Slums are very basic. If you're struggling, you can use one of the Gangsters as a starting character and recruit some gang members to fight on your behalf.
Once you've completed all three levels of the Slums, the achievement will unlock.