Here is the full list of all 28 UFO2: Extraterrestrials achievements.
Eliminate UFO swarm leader
Shoot down 25 alien ships
Kill 50 aliens
Win mission in 10 turns
Finish game on any difficulty
Finish game on hard difficulty
Kill 500 aliens
Shoot down 100 alien ships
Shoot down alien battleship
Capture live alien commanders
Build 3 bases
Build ship base
Build 15 defense buildings
Clean alien base
Throw 100 grenades
Fly 15 planes on the globe at the same time
Reach Colonel rank with one of your soldiers
Win 100 missions
Shoot down Alien Massive Patrol Vessel
Build 5 bases and 3 naval bases
Burn area of 150 fields during one mission
Kill 3 aliens in one shoot
Finish terror mission with less than 2 civil casualties
Finish mission without being seriously wounded
Finish mission without being hit
Collect 3 alien keys
Collect 4 alien crystals
Teleport 10 times during one mission