Mines are destroyed in two ways: Using the red switches to shoot at the mines or sending the directional guys into them. The directional fellas are not affected by the mines. There are several levels including Level 19 that require you to destroy mines. You can redo the levels to unlock this achievement. Crashing into a mine ends your run; its explosion won't be counted towards the achievement.
If you had destroyed enough mines prior to the update, you can open the XBOX app on your phone or PC and this achievement will unlock for you without having to open or even redownloading the game.