Of course, be sure you're playing on Classic difficulty. I'm sure the trophy can be had on Impossible but if you're that good you don't need this guide anyway.
This one was driving me nuts until I was spamming Mission Control looking for UFOs to shoot down (grinding for Shooting Stars
) when I had to let one go and eventually lost a satellite. It turns out I had been confusing Terror misions with Abduction missions. It seems Abduction missions only
become available in a country without satellite coverage. You won't have to wait long after your satellite goes down for a Very Difficult abduction mission.
Before heading out, set up your loadout for all offense. Scopes and 'nades all around! If your earlier in the game favor Heavies and Assault. Two of each if you can. If it's later on and you have Snipers with In The Zone
get them in there. They are absolute gold and they can be good for as many as 4 kills each per turn if you get them positioned right. You'll find clearing out the aliens in five turns is very doable. All in all not a tough trophy once you know what to do.