Go on to any rally point on any mission which has a pelican in it.

Once you see the pelican, throw a plasma grenade or two spike grenades (anything else won't work) at the cockpit.

If your throw is accurate, the blast should send the pilot flailing out of the cockpit and the pelican will plummet down to and right through the ground.

Make sure you put some distance between you and the dropship, because anything inside or underneath the pelican (including you) will be killed.