Here is the full list of all 62 Stars in Shadow achievements.
Build 6 Mines on one planet
Build 200 vessels in one match
Colonize 25 planets in one match
Build 6 Labs on one planet
Build 6 Factories on one planet
Build 6 Markets on one planet
Grow a colony to 25 population (that is not Gaia)
Successfully invade a planet
Destroy a colony with orbital bombardment
Build 100 improvements in your empire
Colonize an Inferno world
Colonize a Barren world
Liberate a Pirate-guarded world
Assimilate a refugee population
Get a Minor Faction to join your empire
Win a Galactic Council Victory
Win as the Phidi Combine
Create an Outpost at a Gas Giant
Colonize a Paradise world
Win a tactical battle
Win a space monster engagement
Discover Gaia
Hire a mercenary
Liberate an enslaved population
Refit a vessel
Establish a colony on a planet with a primitive species
Establish a colony
Defeat a Marauder base
Eliminate a Major Faction
Establish a colony on a planet with a derelict colony
Win a Conquest Victory
Win an Allied Victory
Build a Dread Star
Build a Super-Dreadnought
Enslave one of your own race’s population
Win as the Ashdar Colonials
Win as the Ashdar Imperials
Win as Humanity
Win as the Gremak Empire
Win as the Orthin Conference
Win as the Yoral Khaganate
Build 6 Farms on one planet
Sign 6 different Trade Charters in one playthrough as the Phidi
Sign 6 different Research Agreements in one playthrough as the Orthin
Capture an enemy vessel
Destroy 100 enemy vessels in one match
Win a game on Hard difficulty or higher
Win a game on a map with more than 80 stars
Build 6 Dread Stars in one match
Research every standard technology in a single match
Capture the Gremak homeworld as one of the Ashdar factions
Capture Ashdar Prime as the Gremak
Win a Conquest Victory as the Phidi
As the Gremak, perform Experiments on slaves of 6 different races
As the Gremak, convince a Marauder company to join your empire
As the Phidi, hire mercenaries from 5 different free companies in one match
Win an Allied Victory without eliminating any major factions
Win a game as the Tinkers
Meet the Herald
Harmonize colonists
De-Harmonize colonists
Find and reconnect lost Tinkers refugees