This a very simple one to get.
1. All you have to do is enter the multiplayer menu, choose Custom Games
and pick any game (Halo 1, 2, 2A, 3 or 4).
2. Next Choose Map
and pick any map
3. Then Choose Game Type
section you'll want to look to the bottom of the screen for File options
next to it (this is standard across all control schemes).
4. Click the right analog stick and you'll then get a prompt to Save As
5. Next You enter the Game Type Name
and then Description
and the game will save the new game type.
You can repeat steps 3-5 four more times making sure to change the Game Type Name
for each one in order to get the achievement.
Hope this was helpful to you all.
Thank you to Turtle Mushroom
for the correction on the multiplayer menu.