While you could knock this out at the same time as
It's understandable if you don't want to devote the time to that, as it can take several days even if you are devoted.
Because of this, if you're only going for this achievement I would recommend the "Get in the Ring" playlist.
It is one of only two three-mission cross-game playlists, and I believe it is the shorter of the two.
The first level, "Halo", has a par time of twenty minutes, and you can't really cut too much off of that. The only real way to cut off time is to kill the marines at the later landing zones so you don't have to kill the Covenant there.
The second level, "Delta Halo", can easily be rushed. If you leave the initial zone instead of waiting for a warthog, you can activate the bridge and rush through the level in a ghost. Make sure you kill an Elite before going into the control structure so they don't steal the ghosts. Wait to shoot until you're close to the building so they don't run straight for them.
You can get this mission done in 5-6 minutes.
The third level, also called "Halo", is another where you can't really cut off much time. Depending on how you do during the warthog gauntlet it'll take around 17 minutes.