This can be done on any mission except the prologue (Mission 1: A Personal Contract). There are different "areas" in the missions which act as main checkpoints. Go through an entire area without ever being spotted and this achievement will unlock upon the next checkpoint or completing the level (if there was none after). The first time you can get this is in Mission 2: The King of Chinatown. To the right of the area where the target is, there is a area with chefs and they are selling food. Find the chef with the red apron (a female). Behind her is an odd looking dish with poisonous fish. After she turns her back, grab it. Now go North to where there is 2 chefs and a police guard. On the right, sneak in and find the disguise near the garbage. Walk to the middle area where the target has likely left. Poison his coffee and walk away. After he goes back and drinks the coffee, you are free to exit the level. You will also get the "Silent Assassin" achievement.