You can do this by yourself easily enough.
First, make sure you are playing on the Dry Ice Quarry and then set the AI to Drowning Doom on Brutal difficulty. Don't worry about creating any units or capturing geysers, just keep upgrading your stage. Keep an eye on the enemy and destroy any unit that aren't Grave Diggers. By the time you have finished upgrading and creating a Brood, the enemy should be on its way to your stage.
Since you focused on destroying all the single units, they should have at least 3-4 groups of Grave Diggers so it won't be hard to hit six. Hop in your Brood and focus on the largest group of enemies. Line the carriage up and press A to fire. Hopefully you hit your target and the achievement unlocked.
This method is also effective for the 'Euthanasia' achievement.