Here is the full list of all 66 Galactic Ruler achievements.
Complete Tutorial Chapter 1
Complete Tutorial Chapter 2
Complete Tutorial Chapter 3
Complete Tutorial Chapter 4
Choose your first faction
Win as the Earthers on Very Hard military
Win as the Disciples on Very Hard military
Win as the Swarm on Very Hard military
Win as the Plodders on Very Hard military
Win as the Omniphage on Very Hard military
Win as the Epitaph on Very Hard military
Win as the Osmian Hive on Very Hard military
Win as the Stelloptare on Very Hard military
Win as the Breel on Very Hard military
Win as the Laxan on Very Hard military
Win as the Gulthian Republic on Very Hard military
Win as the Raptyren on Very Hard military
Win as the Onning on Very Hard military
Win as the Dicapse on Very Hard military
Win as the Rhydandites on Very Hard military
Generate your first galaxy
Build a spaceport on your homeworld
Discover another race
Discover a player race in a Multiplayer game
Move a crate to your colony by way of your transport ship
Survey a planet
Survey 1000 planets
Survey 100,000 planets
Build an Orbital Station on a world other than your homeworld
Build 100 Orbital Stations
Build 1000 Orbital Stations
Colonize a habitable world
Colonize 100 habitable worlds
Colonize 1000 habitable worlds
Build an Outpost on a Hostile Atmosphere World
Build Outposts on Hostile Atmosphere Worlds 1000 times
Build an ore harvester to exploit an asteroid
Have 100 harvester minions in a single game
Deploy a beacon
Deploy more than 250 beacons in the same game
Deploy 10,000 beacons
Make 1000 FTL jumps
Fully explore another star system
Fully explore 1000 systems
Fully explore 100,000 systems
Unload units onto an inhabited planet
Capture a crate floating in open space
Capture a beacon
Destroy your first enemy spacecraft
Capture a pirate spaceship
Capture a spaceship of a minor faction
Capture a spaceship of another major faction
Capture the orbital station of another major faction
Conquer a pirate homeworld
Conquer a planetary colony
Conquer the homeworld of another spacefaring race
Fully conquer another planet
Go to war with two major factions at once
Go to war with three major factions at once
Be at war with all 14 other factions at once
Defeat 10,000 pirate units
Lose ownership of a colonized planet
Trade for Galactic Map information from an AI faction
Trade for Galactic Map information from a human faction in MP
Set up a 2 way research cooperation trade treaty
Complete the technology tree