Make sure you are on the correct play list in custom games. This should done in the Halo 4 playlist under custom.
Load up a map. Choose a game type.
Once the game starts hit
and choose end game from the menu.
Once you are at the battle stats screen hit
, then back all the way up and choose the next map and game type. Do this 4 times for the achievement.
You might want to combine this with different game types to knock out other achievements.
These are retro active, you might have to play one game to have it pop.