For this achievement you must complete 3 Halo 3: ODST playlists. Here are the 3 playlists I would recommend completing.
1) Arena Battles - This is the shortest Playlist having only 2 missions (ONI Alpha Site & Coastal Highway) and it's on Normal difficulty.
2) Halo 3: ODST LASO - This is for another achievement anyways so you could knock 2 birds out with 1 stone. If you do not want to play LASO you can always find someone who is willing to give you their checkpoint and it will still give you progress towards this achievement. If you do not want to do either, then read the bottom.
3) Halo 3: ODST Legendary - You have to beat the game on Legendary anyways and there is an achievement for completing the game on Legendary under 3 hours. You could use this playlist as your legendary run and hope to knock out both achievements. If you don't get the 3 hours you can always go back using mission select but again you can knock out another playlist by doing something you already have to do.
If neither of these playlists interest you, then you could do Vehicle Rally or Halo 3: ODST Casual.