In order to get a 3x multipliers, you need to kill one (or more) enemies within the first 5 seconds of the level loading.
25 of these will earn you the achievement, however at the moment this seems to unlock for everyone (I know) at 5. If you head to the safe-house and press the Stats button, you can see how many 3x multipliers you have already.
Bearing this in mind, you still need to be able to kill enemies quickly in this sometimes slow responding game. My tip is to wait until you get your first Orange contract (no, not on your mobile phone *sigh*) it appears in the bottom right of the map and is called "Calm Before The Storm".
Equip the Hunting Rifle as your primary weapon and the Tranquilizer Rifle as your secondary. When the level loads you'll be pointing at the boss, do not try and shoot him like this, you will not kill (unless you fluke a headshot). Instead aim down-left of his feet at the red barrel behind the car. if you shoot it within 5 seconds you will kill him and get the 3x multiplier. You will also get the game over screen (as he is not meant to die) and return to the map where you can replay the mission again.
If anything goes wrong, just forfeit the mission and start again. This makes a very easy 25 (or 5 for now) 3x multipliers.