This one can actually be achieved much easier than previously thought. Whether it is intentional or accidental given the dev team has mostly stopped regularly updating the game since December, could be changed in the full release.
Anyway, instead of relying on drop damage and timing to achieve the 20 kill requirement, simply use the Auto-Turret found in the equipment options. You can swap this out instead of the normal ammo/equipment drop but it functions the same way, falling from orbit after you call for it.
All kills the auto-turret achieves during the active duration count as supply drop kills. This even works in relation to the "Precision Strike" achievement asking you to kill a T-Rex using a supply drop.
Obviously this is MUCH easier than the previous methods and 20 kills is attainable in 2-3 deployments easily. The auto-turret has a fairly quick cooldown so this can be achieved within a single mission.
Happy hunting!