Here are two ways to kill the targets for the Silent Assassin Rating:
-Poisoning the drink
-Disguising as the Red Dragon Negotiator
Poisoning the drink
(You have to take care of the Red Dragon and take his amulet before doing it) To use this tactic, you must go to the sewer near the restaurant to pick the rat poison. Go to the basement, and pick the lock. After that, take the chef disguise. Sabotage the gas so the real chef can go to the basement to check it out. When the chef arrives in the basement, knock him out (because only one chef is allowed to be in the kitchen, it is clear that the chef can also blow your cover. So it will be good to take him out). After that, pick up his key and go to the kitchen. Poison the drink with the rat poison and serve it on the tray (you also have to be careful not to be seen by the bartender, because he can see through your disguise). Ring the bell and hide behind the wall. The bartender shall bring the spiked tea to the targets. After the targets die, go to the second floor without being noticed by the bartender and place the amulet on the table. Escape through the kitchen again without being noticed, and you free to go to the escape point.
Note: There is an easier and quicker way; you can take the amulet out and place it on the serving tray before placing said tray on the counter for the bartender to pick up. Furthermore, it is possible to syringe the chef in the kitchen. First you must get the grounds watching the kitchen door to look the other way, then you pick the lock. Wait until the chef's back is to the door (he slowly turns in circles as he works) and the bartender is talking to the guard, then open the door and sneak up behind him.
Disguising as the Red Dragon Negotiator
This method is a little more complicated that the first method, but comes more naturally if you have played the equivalent mission in Codename 47. First of all, you have to go to the basement to take the chef disguise. Now go and assassinate the Red Dragon, but don't take his disguise yet. Climb through the window and place your guns in the bathroom (the chef disguise will be needed because everybody will blow your cover if you climb the windows with your suit. So you must use the chef disguise to go through the window). And after that, go back to where the Red Dragon's body is. Take his disguise and take his amulet. Go to the restaurant from the front door. The cops shall take your weapons here (so that's why you have to left them in the bathroom so they can't take it away). Enter the restaurant and talk to the bartender. He shall give you the key to the bathroom and you can go there to take your weapons. And finally, go to where your targets are, and kill them all with your guns. Now exit to the entrance and go to the escape point.
Silent Assassin speed run
You need to run all the time and strictly follow this order of actions:
Drop the suitcase as you start running. Go right towards the kitchen back door and pick the lock (but don't open the door). Now run to the basement, pick the lock, take the disguise and sabotage the gas. Skip the cutscene and run to the sewer where the Red Dragon negotiator is taking a leak. Fiber wire him, pick up the amulet and drop his body in the sewer. Now take the poison from the sewer marked ! and run to the kitchen - the chef should be standing in the basement now - and poison the drink and place the amulet on the tray. Then place the tray, ring the kitchen bell, hide behind the door as you wait for the bartender to pick up the tray and run to your exit point. Before you reach the exit, the bartender should have taken the tray up and both targets should have died. Escape and get GK17 dual for the Silent Assassin rating.