You'll get this over time as you're playing multiplayer, blitz, and skirmish(Update, apparently Skirmish counts again!
Skirmish does NOT count, thanks to multiple reporters for verifying!), but if you want to boost it you just need to use these units against enemy infantry.
Also, if you're boosting with a friend in a private match, Strongholds where you leave one Stronghold uncaptured goes into Sudden Death and you have lots of time to do these achievements for specific kills.
Also note, sometimes if any other type of unit happens to hit your target, then it seems to cancel out the 'kill' for the purposes of this achievement. Sometimes it seems like you have to get the kill 100% with the anti-infantry unit.
UNSC:any Hellbringers
Sniper
***any Warthog--this unit even though showing definitely as being good against infantry, doesn't COUNT as anti-infantry according to Adny.
Additional UNSC units that 'might' count for this achievement because they are good against infantry:
Banished:Elite Rangers
Suicide Grunts
***any Chopper -- same as above, this unit probably does NOT count
***any Marauder -- same as above, this unit probably does NOT count
Additional Banished units that 'might' count for this achievement because they are good against infantry: