**Largely copy-pasted from my Ashes to Ashes solution**
***Note: This achievement used to be glitched for some people, but it has since been patched. If you've already fulfilled the criteria, it should pop as soon as you load up Halo 4. Otherwise, proceed to unlock it as normal.****
The maps you need for this achievement are: Outcast, Perdition, and Daybreak. The following gametypes are the ones that you'll need to search for: Daybreak and Perdition show up on Team Action Sack, and Outcast shows up on Dominion.
All other game types either don't feature these maps, or do not allow you to fill up the game with a single Halo party. This will mean you'll have to deal with randoms entering your game and making things more difficult, if not impossible, to achieve.
Anyway, to guarantee that you'll only see those maps, you or someone in your party must delete all other map packs from your hard drive. Matchmaking won't search for maps unless everyone in your party has them. This means that if some combination of players don't have the other map packs, only Castle map packs will show up in the Voting for Maps screen.
To make sure everyone has the Castle maps, start up a custom match, any game mode, on any Castle map. After the mission starts, see who couldn't load the map. They're the ones who have to either download or redownload the map pack. Just keep trying again if someone can't load, and then you're free to start searching in matchmaking.
Once you've got everyone, head over to Team Action Sack for Perdition and Daybreak. Thankfully, you only need six people to fill of your game lobby. That means you can go for this and certain other achievements with as few as two and as many as six other people, depending on guest controllers. That makes it lot easier to set up a session, doesn't it?
To unlock this one in as quick as you can, look for Lightning Flag on Daybreak. Other game types like Fiesta Slayer and/or Binary Slayer don't spawn vehicles, so skip those. Lightning Flag is an interesting game type in that you all have unlimited sprint and you do a ton more damage than you normally would. One shot with your starting weapon will instantly destroy a mongoose or ghost, and two shots will do the same thing to a warthog or banshee.
Each base regularly spawns a mongoose, ghost, and warthog. There are also vehicle spawns in neutral areas as well. Some people in my party found a banshee, but I only bothered with the mongoose. Just meet up in the middle and fire away. This achievement has not been reported as overly glitchy, so you should unlock the achievement without even having to reload.
Remember, an enemy must be piloting the vehicle when you destroy it in order for it to count. You can't just destroy an empty vehicle or one that your ally is driving.