Completing the Finish Them medal can take a little time as this challenge requires “kills” and not “eliminations.”
The most fun way to do this is to open up a solo custom Horde game and turn of the bots so they don’t steal your kills. Start up a beginner difficulty match, choose Del for the auto-turrets for passive kills, and have fun.
The fastest way to rack up clean kills is to make it to wave 10 in Horde and pray you get the Carrier boss spawn. If you don’t get him, quit out and run through it again.
Once you finally get the Carrier boss to swan, instead of killing him, destroy all the other bots on the playing field and walk him around the map.
The Carrier will continue to shoot out his spawn projectiles, and all you have to do is keep killing them as they are shot into the sky. Shooting the projectiles actually counts as kills, and they only take a handful of bullets. Choosing Marcus is an easy decision as he auto-regenerates bullets.