Heres a video guide if you don't want to read the essay below
Head to the Armory and look for the Grenade Disposal on the right side of the room. Throw 30 grenades into the hole to unlock the achievement.
This is much easier offline as you get all the credits and use them to buy grenades. Best thing to do is use all your Timed grenades then buy the Contact Grenades and Teleportation Grenades from the Armory.
Try run around the Cargo Bay to kill all the zombies but leave two alive (Crawlers are better) then return to the Armory to restock and use the disposal. Aiming the top line of the crosshair just above the hole got the grenades in most times for me.
I'm not the best shot with the grenades and managed to get this by round 11