To perform a Drop Assassination you must drop on an enemy from above and press just before landing on them. You will always see the button prompt come up as soon as you are within range of performing the assassination.
The easiest place to perform all 5 Drop Assassinations—very early in the game no less—is during Mission 2: High Overseer Campbell. After starting the mission head to the waypoint that says “Granny Rags” at the end of the street. Blink up to her apartment and speak with her to get the side mission “Gentleman Callers”. Three thugs will then begin to bang on her front door demanding that she let them in.
Walk upstairs to the patio that you entered to and enter stealth mode by pressing . Climb onto the railing and save the game. The reason for this is that if you mess up you will be able to immediately load and try again. After you are done saving, perform a Drop Assassination on any of the three thugs. Immediately after you do, Blink back up onto the patio and repeat the process until they are all dead. Now head around the corner to where two more thugs have Griff trapped in a building.
Blink up to the pipes and traverse the building until you are just above them. You can save here again as well. After saving perform another Drop Assassination and then blink over to the rocks just to the right of the building. Jump off of the rocks and perform the fifth and final Drop Assassination to unlock the trophy.
You will come across many opportunities to perform Drop Assassinations throughout the game, so if you do not utilize the method above you should still be able to perform 5 throughout the rest of the missions.
To see a complete walkthrough, please see the video below: