Here is the full list of all 11 Galaxy of Trian Board Game achievements.
Win the custom game against one AI opponent
You won a game with score 100 victory points or more
Win a game with a score 200 victory points or more
Win a game with a score 300 victory points or more
Win a game with a score 400 victory points or more
Win a game with a score 500 victory points or more
Win a game with a score 1000 victory points or more
Finish your training by completing the campaign
Win a game against two AI opponents
Win the toughest game - against three AI opponents
Challenge a random opponent in the network game (or be challenged) and win such a game