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 which has
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 As5. 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.
***EDIT***
Thank you to
Turtle Mushroom for the correction on the multiplayer menu.