Here is the full list of all 93 Endless Space - there are Collection achievements.
Level up a Hero to level 10
Explore 75% of a huge galaxy in less than 40 turns
Colonize a Garden of Eden - by groovytadpole
Play for 10 turns
Clone Galdos AI - by Adder
Have a Trade Route with every other system in the galaxy - by Nosferatiel
Win with the Amoeba
Win with the Automatons
Win with the Cravers
Win with the Hissho
Win with the Horatio
Win with the Pilgrims
Win with the Sophons
Win with the Sowers
Win with the United Empire
Win a Diplomatic Victory
Win an Economic Victory
Win an Expansion Victory
Win a Science Victory
Win a Score Victory
Win a Supremacy Victory
Win a Wonder Victory
Win a game in Normal or higher difficulty against AI
Win a game in Hard or higher difficulty against AI
Win a game in Serious or higher difficulty against AI
Win a game in Impossible or higher difficulty against AI
Win a game in "Endless" difficulty against AI
Win a Supremacy Victory with the Cravers
Level up a Hero to level 20
Build 100 improvements in your entire Empire
Build 250 improvements in your entire Empire
Build 500 improvements in your entire Empire
Use every Battle Action of a Hero at least once
As Horatio, own 10 tiny planets with at least 10 population
As Amoeba, win a game without building any ships containing weapons
As Automaton, have 10 systems with the max FIDS bonus from Orbital Platforms
As Cravers, have your home planet not depleted at turn 80, without having lost your home system
As Hissho, build 1 000 ships on systems with Wargame Center while Bushido is active
As Pilgrims, colonize a system with a Fleet Errant containing Factories of the Faithful
As Sophon, receive 30 technologies from others and give at least 30 technologies to others in a single game
As Sowers, win a game without building any Food improvement
As United Empire or Sheredyn, own at least 20 deposits of one of the Strategic Resources in a single game
Have 1 system which produces more than 1 000 dust
Have 1 system which produces more than 1 000 food
Have 1 system which produces more than 1 000 science
Have 1 system which produces more than 1 000 industry
Win with a Custom Faction
Create a Custom Faction with 0 points or less and win a game with it
Create a Custom Faction with -100 points or less and win a game with it
Create a Custom Faction with -195 points or less and win a game with it
Win with a Random Faction
Terraform a planet to your home planet type - by EvilTactician
Be the only remaining empire in a game with 8 starting empires - by Monthar
Envelop another empire's system in your Influence Area - by FreeMarket
Be the faction with the highest score at turn 25 playing on hard or higher difficulty
Be the faction with the highest score at turn 50 playing on hard or higher difficulty
Be the faction with the highest score at turn 100 playing on impossible or higher difficulty
Travel 10 000 parsecs in all your games
Travel 100 000 parsecs in all your games
Travel 1 000 000 parsecs in all your games
Explore 25% of a huge galaxy in less than 25 turns
Explore 100% of a huge galaxy in less than 50 turns
Win with an Expansion Victory with the Sowers when you have the Endless Hero
Hire the Endless Hero
Unlock the whole Diplomacy & Trading tech tree in a single game
Unlock the whole Exploration & Expansion tech tree in a single game
Unlock the whole Galactic Warfare tech tree in a single game
Unlock the whole Applied Sciences tech tree in a single game
Destroy 5 enemy fleets within a turn
Destroy 10 fleets within a turn
Destroy 15 fleets within a turn
Play for 1 000 turns
Play for 10 000 turns
Build every Improvement in your home system - by Divine_Moments_of_Truth
Win with the Sheredyn
Create a custom faction with -195 points or less, and win a game with it on Endless difficulty
Hire the two romantically involved heroes, the spy and the general, in the same game.
Destroy 10 colony ships using Battle Stasis
Kill 50 populations via Bombardment
Destroy 50 improvements via Bombardment
Win with the Harmony
Successfully carry out 5 land invasions during the same turn
Use every fleet formation
Use every fleet targeting option
Kill 10 troops with collateral damage
Kill 50 troops with collateral damage
Kill 200 troops with collateral damage
Destroy 50 Fighters and Bombers
Destroy 200 Fighters and Bombers
Destroy 500 Fighters and Bombers
As the Harmony, purify 10 systems in a game
Win a Supremacy Victory by capturing 4 home worlds within the same turn
…the galaxy as the Archivist, Emlek Tarosh, fulfills its duty.