Enemy parachutists are dropped out of bombers or airships.
If you are given a mission to prevent enemy bombers, fly to where they are but don't shoot them down. Eventually they will get to their target and start dropping paratroopers. Simply follow behind the bombers and kill the parachutists in a line.
Alternatively, if you shoot down an airship, as it sinks to the ground it too will deploy paratroopers. The reason this trophy is easier with the bombers is that you might have four bombers deploying paratroopers at once, rather than a single line from the airship. Nevertheless, both can give you the chance to kill 20 in 20 seconds.