This can be earned in local or online play as long as your teammate is alive at the end of a Team Deathmatch game. This will likely unlock when earning "Online Multi-slayer," but if it doesn't or you want to earn it prior, the easiest method is detailed below. You do not need to survive in order to unlock this achievement. As long as your teammate is alive and your team wins, you will satisfy the conditions for the achievement regardless of the status of your general.
Start a Skulls Local game of Team Deathmatch with four players, unlimited time, and on the Murky Mire map. Note which color your primary profile is and the color of your teammate. When the game starts, simply have the opposing generals rush toward your teams and get killed. The game will be over and the achievement will unlock in roughly four turns of each team, or fewer if you meet the opposing generals mid-way across the battlefield.
If you do this in a local game as opposed to asynchronous online play, you will need to repeat it for each device.