Here is the full list of all 13 Mini Gal4Xy achievements.
Get 3 stars with Ktulus
Get 3 stars with The Empire
Get 3 stars with the Fermulons
Get 3 stars with the Nomads
Get 3 stars with the Brains
Get 3 stars with the Pandarus
Get 3 stars with the Pirates
Get 3 stars with the Cephalloids
Get 3 stars with the Arnachids
Get 3 stars in a Short Game
Get 3 stars in a Long Game
Get 3 stars in a Very Long Game
Get 3 stars in a Marathon Game