You will run into your first Assassin—masked enemies that can vanish and teleport like you—during Mission 3: House of Pleasure. After speaking with Slackjaw you will exit the distillery and take a right, instead of going towards Granny Rags’. Three Assassins will then appear out of thin air to ambush you. Simply use Blink to appear directly behind one of them and then quickly turn and attack them with your sword. They will have lost sight of you which gives you the opportunity to assassinate them. This method works with every enemy type and allows you to quickly dispatch them with minimal effort.
If this sounds too complex or you are already beyond this point in the game, there is no need to backtrack, because they appear several more times in the game. During Mission 7: The Flooded District you will finally battle a number of Assassins. You will have dozens of opportunities to assassinate one, but I suggest doing it while you are unlocking the This Is Mine trophy, which you can refer to for a complete walkthrough and the location to assassinate an Assassin.