You can get this achievement at the end of the tenth mission called "Clockwork". As with every other misc. achievement in this game you can play the mission on the easiest difficulty setting and still get it!
At the end of this mission you'll get out of the base in a vehicle. You'll be at the turret. By pressing the Y button you can switch between a grenade launche and a minigun. For the achievement you should stick to the grenade launcher.
After you got out of the base and past the first two parked cars you'll be driving on a frozen river. Using your grenade launcher you can create holes that enemy vehicles will crash into. While the achievement say you have to drop 8 vehicles this is not really the case. As long as they get destroyed by one of the holes you're golden.
Just try to shoot in front of the cars and snow mobiles. There will be dozens of enemy vehicles during this section so it shouldn't be a problem getting the 8 of them destroyed. Always aim in front of them and when you see them getting destroyed you already got one more.
*Note: Video was taken on the 360. I can replace it with a video taken on the One but I don't want to put two copies of each achievement on my YT channel. If somebody would rather see an Xbox One video let me know and I'll happily provide one for you. Thanks for reading*