Make sure you take your sniper for this mission.
When You first enter go to the desk area to your right and talk to the clerk, she will give the card to your room.
Next, run to the elevator to your left up the stairs, climb the hatch, pull out your fiberwire and wait for your first target to arrive.
As soon as he gets in and the doors close preform a strangle.
Take his keycard but leave the suitcase and head to your room on the 7th floor.
When in your room,go to the balcony, unload your sniper and wait for your next victim to enter his room to your right when you first enter the balcony.
He should walk out on his balcony and you can easily shoot him in the head.
After this is done you can head towards to the eighth floor, towards your first victims room.
Be sure to pull a fire alarm before you enter his room to make his bodyguards leave, but hurry and run into his room as they will come back.
You must then run to the room furtherest to the back of his room where on a table a phone will say redial, and press as it says.
This will make your third target enter an area just below the balcony of your room on the seventh floor so rush back, unload your sniper and when he comes out boom - headshot!
If done correctly without any other kills you should earn the silent assassin rating.