Head over to Mr. Fuk's Rice Box in Alderney. Walk up to the door of the restaurant but don't go in. Then go to the back of the restaurant and use a Rocket Launcher or a Grenade to blow up the car and motorcycle (this will make the mission easier at the end). Head into the restaurant and kill the man behind the desk. Go to the right entrance to the restaurant and gain cover. Kill Kim's goons but watch Niko's health. A grenade or SMG would be useful here. If available, Dwayne's friendship ability (two gangsters providing backup) may be useful, as you will likely be taking fire from several directions at once.
Once all the goons are dead, go into the manager's office. There is a choice here: kill the manager to save time or threaten him into a conversation. Either way, the game prompts the player to look for Kim in the kitchen. Kill the goons that respawned with an SMG or Micro-SMG then run into the kitchen. There will be a small number of goons in the kitchen, end them and run after Kim. He will run down the fire escape and try to escape in a car.
If you blew up the car in the beginning of the mission, Kim will escape on foot, meaning that you can stay on the fire escape and kill him with an SMG or Sniper Rifle. Or, you can use a car bomb provided by Patrick McReary to explode the car, if available. Just put the bomb in the car, continue the mission, and when Kim escapes, detonate the bomb.
Jon Gravelli will call after the mission and say that Niko did an amazing job.