All of the 'Faces of Killed' achievements rely on exactly the same principle, it's just a matter of the length of the killstreak that you build up.
From the Main Menu, look at the Movie Shelf and highlight the movie called 'Faces of Killed 3' (it's on the third row down). It may also be called 'Yo! Skullface!' depending on your game settings.
You'll be thrown into a mini-game (which is a good place to make some money as well, coincidentally) that is all based on your reaction times and a small dose of luck. You'll see a bar appear at the bottom and a segment of that bar will show up red. You simply have to press
when the arrow slight above the bar is over the red section.
Doing it once, will count as 1 in the chain, and you'll see a gory kill in the background (unless you're on PG settings).
Doing it 5 times in a row without failing will unlock this achievement.
There is also no timer for this, so you can take as much time as you want in between each kill.