Here is the full list of all 90 Terra Invicta achievements.
Control a fleet with over 9000 combat strength
Build a ship with 4G combat acceleration
Build a ship with at least 1000 kps
Build a Titan
Colonize Jupiter
Control 42 Habs
Assault a Hab with marines
Destroy a megafauna
Learn your faction's victory conditions
Initiate your first interplanetary fleet transfer
Assemble a fleet of 10 ships
Build a station at a Lagrange Point
Win a space battle without losing a ship
Control 20 Nations
One of your councilors dies of old age
Lose a space battle by having all of your ships destroyed
Refit an existing ship
Conduct an orbital bombardment
Control 6 Councilors and have 2 turned Councilors
Sabotage a Faction's research
Steal a ship from another faction
Recruit a full council of 6 councilors
Destroy an Alien army
Fire a nuclear barrage
Research Exotics
Have one of your countries declare war on another country
Win a space battle
Steal a station from another faction
Colonize Venus
Colonize Mercury
Build your first ship
Capture an Alien
Upgrade a ship class
Research Pherocytes
Impose Regime Change on a nation
Kill an Alien
Assassinate a councilor in space
Colonize Mars
Have a councilor equip 25 stars' worth of orgs
Successfully Purge an Executive CP from another Faction
Trigger nuclear winter
Steal a technology
Build a habitat on the surface of a spacebody
Research Alien Movements
Turn an opposing councilor
Complete a successful Coup d'Etat mission
Build a habitat in space
Kill an opposing councilor
Capture a Enemy Councilor
Investigate an enemy counselor and learn their loyalty
Augment your Councilor
Send a councilor into hiding
Complete a Trade with another Faction
Obtain control over a nation
Investigate an alien crash site
Start your first campaign
Win as the Resistance
Win as Humanity First
Win as Project Exodus
Win as the Initiative
Win as the Academy
Win as the Protectorate
Win as the Servants
Win on Normal Difficulty
Win on Veteran Difficulty
Win on Brutal Difficulty
Win with all 7 factions on normal or greater difficulty
Destroy a Mothership
Have one of your stations stolen by another faction
Have one of your ships stolen by another faction
Colonize Luna
Colonize Ceres
Colonize Io
Colonize Europa
Colonize Saturn
Colonize Mimas
Colonize Uranus
Colonize Miranda
Colonize Neptune
Colonize Pluto
Colonize Haumea
Colonize all Major Planets
Control a launch facility on earth
Research all Techs
Control a Megafauna
Win as Resistance after Servant or Protectorate Win
Fail a mission with where you have greater than 99% chance of success
Escape an alien fleet in pre-combat
Cause Earth's sea level to rise 2cm
Control a nation that completes a nuclear weapons program