Here is the full list of all 27 Star Dynasties achievements.
Design a family of 16 characters
Win the game
Customize your character
Raise a child from birth and have them come of age with a skill greater than 50
Fully acquire a bloodline upgrades branch
Have a league of 30 systems
Have an affair
Have 250 money
Conquer your first system
Win a battle
Have a league of 15 systems
Win a tournament
Complete 20 turns in one game
Press a claim
Have 10 house members assigned to a task
Have a baron swear allegiance to you
Repair your first installation
Complete 10 turns in one game
Trigger your first expedition event
Host a feast in someone's honor
Assign a house member to a task
Have all places in your council filled
Have a duke swear allegiance to you
Complete the tutorial
Have all house scores above 200
Have 3 of your children be wards of foreign rulers simultaneously
Have a foreign ruler inherit your house