Here is the full list of all 31 Twilight Struggle achievements.
Win a game as the USA.
Win a game by getting 20 VP before final scoring.
Win a game as the USSR.
Win a game by controlling Europe.
Win a game against the AI Player.
Lose a game against the AI Player.
Gain Domination in a region.
Complete the tutorial.
Win a game in final scoring.
Win a game with DEFCON 1.
Win a game with Wargames.
Win a game via Cuban Missile Crisis.
Lose a game against the AI Player in final scoring.
Win an online game.
Win an online game against an opponent with a rating at least 300 higher than yours.
Win a game in the Early War.
Win a game due to the Victory Point Track when your opponent has Domination in at least 4 regions.
Be the first player in a game to advance in the space race.
Play the China Card.
Headline a scoring card.
Win a game without playing the China Card.
Win a game without ever sending a card to the space race.
Win a game after reaching the end of the space race track.
Win a game after opponent reaches 18 on the Victory Point Track.
Score 8 VP when Southeast Asia Scoring is played.
Gain 3 VP from Arms Race when it is drawn for Missile Envy.
As USSR, gain 3 VP from We Will Bury You while U-2 Incident is in play.
As USSR, gain 6 VP from OPEC.
As US, gain 7 VP from Alliance for Progress.
As US, play "The Voice of America" three times in one game.
As US, play "The Voice of America" during Turn 10, AR8 US.