Toward the later part of Chapter 1, you will be chased by a mechanical dog. After that sequence, you will drop down a shaft and can then jump over a railing to perform a silent takedown. After completing the takedown, simply restart from the latest checkpoint - which will take you right back to the point where you can redo the takedown. Your previous takedowns are saved and counted, even after restarting. Repeat 20 times to unlock the achievement and receive the Eagle Eye perk, which will make collectibles appear on your map.
It should take 10 minutes or less using this method and should also unlock the Vampire perk and achievement.
Credit to rus199410