Now that the Bandanna skull is available to everyone, I found the best way was to turn on Bandanna, Boom, and Grunt Funeral Party on Easy. This way, you can do it without ever needing to fire the sniper rifle.
Switch to old graphics with
, as the new textures occasionally don't behave well with the old textures. From the place you spawn, angle your throws upward to barely clear over the edge. Once it's doing this, slowly pan left and right to carpet bomb the area. This gets rid of the enemies on the far side of the area. These are the enemies easily sniped, so if that's not the problem, take them out from the mouth of the area, by the tree.
The enemies close to the near wall were the problematic ones for me. You'll want to be closer to the wall with a higher arc on the grenades to get them just over the side to get the rest of them. Once you've got that high arc, it's the same process; pan left and right to carpet bomb closer to the new wall. For reference, back in new graphics, there's two darker leafy plants by the path before heading in; that's where I was standing when I got the rest of them.
The achievement pops immediately after the last kill. If you've done all this and the marines charge forward to meet the enemy with a music change, check to see if it isn't stuck in "Done! Unlocking..." as that indicates you've completed the first area.