Beretta 92SD and Knife method
At the start of the mission, go the restaurant, talk to the bartender, and pick up the toilet key. Go to the rest room and drop your Beretta 92SD there. Go out and to the north-east section of the map (near the sewer). Wait for the Red Triad Negotiator to pass near you. Go behind him and kill him with Oyabun knife. Take his clothes and Red Triad Amulet, then drop him to the sewer. Proceed to the restaurant.
When you try to enter, a police officer will search you for weapons. Your Oyabun knife will be taken, but disregard it as it is useless now. Go inside and the Chief of Police will talk to you. After that, go to the rest room. Pick up your Beretta 92SD, holster it, open the door, walk back a bit so that the Blue Triad Emissary is out of your view and aim to the Chief of Police's head. Draw your weapon and shoot him. Holster it again and climb out of the window. Re-enter the restaurant and drop the Red Triad Amulet (if you did the previous instructions correctly, your cover wouldn't be blown. Though, a police officer will frisk you again, taking the Beretta 92SD). Go to the rendezvous point.
After shooting the Chief of Police, you may also wait for a few seconds and then walk straight into the restaurant, drop the amulet and run out, through all the cops, to your rendezvous point.
That's it! Mission complete. Good job, 47.
Mission reward: $15000