The vehicle you start out with already comes equipped with Mines.
To use them, simply swipe your finger to the right. The Mines are set to the right as default, but you can change the slot in the Weapons section of the Garage if you wish.
The easiest way I found to get the achievement was to drive directly in front of someone and use a mine. The opponent won't have time to steer out of the way.
Please comment if you vote negatively. I will edit my solution to make it better.