To perform an assassination, move behind an enemy and hold the RB button. If you just press RB, you'll perform a one-hit pummel and not an assassination. For the kill to count as an assassination, an animation must accompany it.
You can earn this achievement in any mode, but if you want to get this one out of the way, load up the Nightfall campaign mission and assassinate the oblivious Elite at the start. This video is from our unofficial game guide. You can view the full guide here