To earn this achievement, you simply have to kill an opponent in a rocket race game. The Rocket Race game is ONLY found in the "Multi Team" playlist, and this playlist has 12 players in it. Because of the large number of players, it is unlikely that you'll actually play Rocket Race so I recommend getting the largest party you can get (guests are fine) and head into Multi Team. If you get rocket race and you have a friend on the other team, meet up somewhere on the map and kill eachother. You cannot die when you're on the mongoose so the player dying has to get off.
If you do not have any friends in the game, simply drive around looking for red arrows. These indicate players who are not on their mongoose, and therefore are able to be killed.
*Edit - "nel e nel" has this bit of advice for people:
If you don't have friends to boost with, you can use the rocket splash damage to knock people off the Mongoose. Don't hit the Mongoose directly as it will have little to no effect, you want to aim next to it or in front of their path. This will cause them to go flying and tumbling, and if they land upside down they will automatically get thrown off in order to flip over their Mongoose. When they are scrambling - BLAM - hit them with another rocket. Should be pretty easy I got two double kills in under 5 minutes in my first time ever playing Rocket Race.