Here is the full list of all 21 UFO: Extraterrestrials Platinum achievements.
Shoot down 100 alien ships
Eliminate UFO swarm leader
Shoot down 25 alien ships
Kill 50 aliens
Fly 15 planes on the globe at the same time
Build 15 defense buildings
Finish mission without being seriously wounded
Finish mission without being hit
Build 3 bases
Win mission in 10 turns
Finish game on any difficulty
Finish game on hard difficulty
Kill 500 aliens
Shoot down alien battleship
Capture live alien commanders
Clean alien base
Throw 100 grenades
Reach Colonel rank with one of your soldiers
Win 100 missions
Shoot down alien battlecruiser
Finish terror mission with less than 2 civil casualties