Here is the full list of all 62 Stars in Shadow achievements.
Establish a colony
Win a tactical battle
Refit a vessel
Defeat a Marauder base
Liberate an enslaved population
Liberate a Pirate-guarded world
Eliminate a Major Faction
Win a space monster engagement
Establish a colony on a planet with a primitive species
Establish a colony on a planet with a derelict colony
Get a Minor Faction to join your empire
Win a Conquest Victory
Win an Allied Victory
Win a Galactic Council Victory
Successfully invade a planet
Destroy a colony with orbital bombardment
Build a Dread Star
Build a Super-Dreadnought
Hire a mercenary
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 Phidi Combine
Win as the Yoral Khaganate
Grow a colony to 25 population (that is not Gaia)
Build 6 Markets on one planet
Build 6 Farms on one planet
Build 6 Mines on one planet
Build 6 Labs on one planet
Build 6 Factories 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
Colonize 25 planets in one match
Colonize an Inferno world
Capture an enemy vessel
Destroy 100 enemy vessels in one match
Build 200 vessels in one match
Assimilate a refugee population
Discover Gaia
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
Build 100 improvements in your empire
Colonize a Paradise world
Colonize a Barren world
Create an Outpost at a Gas Giant
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