This is a basic story driven part of the game that will come as you go through each area, and they show up in droves on the moderate missions, generally having several per mission. Should only take a hand full of missions to complete.
This is an achievement that can only be missed if you give up playing the game entirely and will happen over time. The Grunt is the most basic of the enemy that is found in the game and they only do melee type attacks. Best to hit them from a distance with a gun or grenade (for the explosives achievement).
Any type of kill on them will count, be it melee, takedown, grenade, fast moving ballistic projectile, whatever you can come up with.