This can be done on any number of missions, but it's best suited for one of the later missions-one of the longer ones with lots of enemies and lots of reinforcements. The grenade launcher (Assault Class) counts towards this achievement, and may be a little easier to use than hand grenades.
An easy mission to do this on is DMZ, at the Eastern Village. You will be facing LOTS of respawning enemies, and you'll have a lot of Assault reinforcements to work with. Just stick with the grenade launcher and keep firing away. There will be more than enough enemies and friendly reinforcements to ensure you get your 20 grenade kills at this part.
Remember, while you'll unlock the achievement immediately, make sure you DON'T QUIT once it unlocks; either finish the mission or just fail...if you quit, it won't save the medal towards your campaign progression!