I've set up a Portal server specifically for this achievement. The server makes vehicle health low and projectiles fly fast.
Equip a recoilless M5 launcher as an engineer, spawn in a helicopter, fly over an enemy helicopter, jump out, equip your parachute, equip the recoilless M5 launcher, then aim and shoot. The rocket flies very fast due to server settings, so there's almost no need to adjust for the vehicle movement.
You can either search for the server "Aerial Hunter Achievement" in the browser, or you can use the experience code ABKKMX, which I would recommend over searching in the browser.
To use the experience code, head to Portal -> Host -> Experience Code (in the top right).