You can play War Machine by going into Multiplayer, creating a lobby, assigning yourself as Germany and playing against the AI. Set the AI difficulty to to Settler to make this a lot easier.
When the game loads, focus your Artillery around the city-state of Luxembourg. Have your Infantry surround the city before attacking, and when you're ready to attack, unleash your Artillery on the city. Luxembourg doesn't have walls and will fall very easily. When it has no health left, simply move one of your Infantry in and the city will be yours.
If done in a single turn, the achievement will unlock.