As you progress throught the game, a popup will tell you that an assassination mission has opened, meaning that now if you go to your map, you can find the crosshair icon indicating the location of the pigeon coop. These coops contain assassination letters for you to follow. After finding one of these coops, usually on the second floor level, you will be assigned to an assassination memory, follow the mission requirements, which can vary from do not be detected to, kill without weapons. Once completed the achievement will unlock.