If you haven't played through the game already, then you'll get this at the end of the chapter "Riding Shotgun". If you have done so already, then start a new game under this chapter. When you are asked to take down the chopper (and it is always you, Gordon Freeman, never anyone else), you'll need to use your Gravity Gun to pick up the mines and toss them back at the choppa.
To earn the achievement, you CANNOT miss with any mines that you throw in the air. All of them must strike the chopper, and you'll know when you have hit it when flames/explosions engulf the chopper. If you miss, then no achievement for you.
It took me a few tried to do this myself, but I made it easier by setting the difficulty on 'Easy', which only required me to hit the chopper three times with mines.
Save right before you start taking it on, and save after each hit. It makes the fight a lot easier, and lessens the frustration factor a bunch.