Go to chapter 2, Evacuation Orders: Dead End. Immediately after you start, a mech (on your side) will go off ahead and start fighting a giant enemy spider thing. Keep sprinting ahead while this is going on, and near a red barrel there will be a rocket launcher, you'll be using this to take down the dropships.
Immediately after you get the rocket launcher, you'll see the first dropship. Shoot it down.
After that, you'll come to an area where a ton of enemies are attacking from the left side. Take care of them, and another dropship will fly in ahead of you. Shoot it down.
After that, an ally's tank will clear a path through a barrier. Sprint through as quickly as possible and two dropships will take off, one after the other. Shoot down both of these, and you're done!
Note that it's actually pretty difficult to shoot these down, since you only really have time to shoot one rocket and the dropships are pretty well armored. Their vulnerability seems to be their underside, so try to get under them and shoot up. If you don't get one, restart the last checkpoint and try again!