To earn this achievement, you'll need to hunt down a guy named Ming, one of the associates working for Dogeyes. This is actually story-related and cannot be missed. You'll find him around the corner of a vendor that you spoke to moments ago, asking for his whereabouts.
Once you spot Ming, a cut-scene will ensue and will go directly into gameplay. Immediately give chase to Ming throughout the market, making sure to get past the obstacles by timing your A button prompts just right. At some point, during the chase, you'll crash through a silver gate and come upon some of Ming's friends, who are going to fight you.
By this point, you should have been acquainted with the basics of fighting, so deal with the thugs as best as you can. Defeat them and put the last thug in a trash bin, then climb it up and continue the chase with Ming. You will finally reach a rooftop, with Ming yelling at his friends to take you on, not to mention joining the fight. Ming is the most powerful of the group, so my advice is for you to deal with the thugs first, take them out, then concentrate solely on Ming, who wields a sharp knife as a weapon. I defeated him by countering his attacks and getting in some shots with my punches. Grabbing is not an option, so stick to your melee attacks and counters and Ming should go down without a sweat.
The cops swarm in, arrest you, a cut scene ensues. Once that cut scene is done, the achievement should be unlocked for good.