These become available after you pay a visit to the Kung Fu temple. The Martial Arts Clubs are displayed as on the map. These require you to defeat 6 rounds of enemies. You do not have to bet on these fights and when you die you do not have to pay hospital fees. Suggest collecting as many Jade Status as you can so that you can learn new fighting combos and moves. Refer to the video below for Jade Statue locations.
Here is a great video guide by Predni showing you all 11 Jade Status and how to get them to appear on your map.
Also try to move around a lot to keep from having the whole gang all up in your space at once. If that happens another guy could easily take you out from behind while you're attacking someone else. Keep as much open space around you as you can and focus as best you can on whichever guy is a little more separated from the others. This goes the same for fights at drug deal locations.
My advice is wait til you finish the game. I went in after I was completely leveled up, returned all the jade statues, got all the health shrines. Also, drink tea and dragon kick beforehand. The tea makes you tougher, and the dragon kick increases the damage you deal. Do all that, and you're pretty much unstoppable. Oh, and counter, counter, counter. Especially against big guys. You're best approach to them is to counter and immediately start throwing at them with heavy attacks.
I can't check this achievement and Big Smiles All Around - yo, admins - is there some kind of problem with it? Actually both achievements becomes unchecked after DLC: Year of the Snake. I don't have that DLC and the checkmarks automaticaly jumps from Martial Law and Big Smiles All Around onto Bomb Squad and Cult Master. Can you fix this, please?