In this mission you have to eliminate the King of Chinatown. This mission is fairly short if you ignore challenges. This guide is just to completing The King of Chinatown mission on the hardest difficulty (purest) without being seen. This guide does not explain how to complete the different challenges.
There is a YouTube video with a visual version of this guide at the end of this guide.
At the start go all the way to the back of the little area and pick up a bottle:
After a while the King of Chinatown will walk up next to you and eat a bit of the food there. Then he will turn around and also stand in front of the open sewers. Walk up to him and kick him into the sewers: