In order to do this, you need to be a tailor with a Magnificent Flying Carpet (Not sure if the slow one works or not).
Normally in the mine area, there are anti aircraft missile launchers that shoot you down if you try to fly in with your mount. However, with the Flying Carpet it doesn't recognize that it's a flying mount.
Also another perk is that normally after one hit, you get knocked off of your mount and fly into the air. While riding on my Flying Carpet I was just able to plow through the mine field without any knockbacks until I got the achievement and then just flew away.
Hope this helps!