UPDATE August 16th, 2019: Irken in the top solution comments has mentioned about picked up heavy weapons possibly counting as vehicles! Avoid those heavy weapons with your main account also. Heavy weapons are the Covenant Plasma turret and the UNSC Heavy Machine Gun.(You go into 3rd person view when holding them)
There is a far easier way to get this achievement if you have two controllers!
Sign-in a guest, and have them use all the vehicles(I've made the mistake of confusing my controllers once, it doesn't work if the guest doesn't get in a vehicle and the main controller does unfortunately). I've discovered that secondary accounts don't teleport into your vehicle fortunately if there's an empty seat!
I used my main account only for hanging onto power weapons for fun, and generally wasting time. This was much easier than I expected. I did it on Normal as part of the Wheels, Wheels,.. playlist.
I killed everything, took the driver and gunner out of the first wraith then used that to slaughter everything past that point as well. I never stepped close to a vehicle or anything you can get in or out of with my main account.
And that's it! I was very nicely surprised with the 'pop' after doing this.
Hey, if you're a pro, you can do it in 4 minutes or less with your secondary controller!! (check out the ridiculously good video on youtube.. )