This is the easiest achievement of the game.
Host a local versus match against three other AI worms teams. Be sure to set the game mode to "Full Wormage"
When selecting a map, scroll to the left and be sure to "randomly generate" a level that is a single island with no roof. One that will make sure every worm can be hit by an air strike
On your first turn, use Armageddon. It should unlock after your first use if every worm is in an open spot.
You might have to wait a minute or two since using Armageddon will trigger one or two game clip recordings and the achievement will usually pop after those do.