A 'Takedown' is a Quick Time Event activated by using the melee button.(you required to press the corresponding button which shows on screen in a set time limit.)

A tutorial on how to do a Takedown is given to you at the start of the first level. Once you kill a few enemies, the guy on the dock can be melee and the your 1st Takedown starts.

Try and obtain as many as you can throughout normal progression of the game by sneaking up or charging enemies.

If you have finished the game and still need some more enemies, head to the level Science Centre Exterior. First, shoot the snipers and then head down to the alleyway. You can melee the first 3 enemies and then open a door and melee another 2. Pause the game and restart from the last checkpoint as that respawns the last 2 enemies you tookdown. Rinse and repeat.