This achievement is very straight forward but can be a struggle to get.
My advice is play game modes that have less players or modes with few lives! Any heroes and villains game modes are good but the best imo is Hero showdown due to the fact its only 2v2 so there is a high probability that you will get the first kill unlike Galactic assault with 40 players, plus bots. If you don't get the first kill leave the game and rinse repeat until you get it, good luck!