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