Here is the full list of all 54 Distant Worlds: Universe achievements.
Destroy 1000 Enemy Troops
Eliminate 1 Enemy Empires
Empire Splits (Civil War)
Build 10 Galactic Wonders
Destroy 100 Space Monsters
Destroy 50 Space Monsters
Capture 50 Enemy Ships and Bases
Destroy 1000 Enemy Military Ships and Bases
Eliminate 100 Enemy Characters
Build 5 Galactic Wonders
Conquer 10 Enemy Colonies
Eliminate 50 Enemy Characters
25 Successful Espionage and Sabotage Missions
Capture 10 Enemy Ships and Bases
Eliminate 20 Enemy Characters
Spend 0% of time at War
Destroy 100 Enemy Troops
Destroy 100 Enemy Military Ships and Bases
Destroy 100 Enemy Civilian Ships and Bases
Destroy 50 Enemy Military Ships and Bases
Destroy 50 Enemy Troops
Destroy 50 Enemy Civilian Ships and Bases
Build 1 Galactic Wonders
Destroy 20 Space Monsters
Mine Most Resources
Highest Trade Volume
Own an operational Planet Destroyer
Break 20 Treaties
Capture 100 Enemy Ships and Bases
Conquer 50 Enemy Colonies
Conquer 100 Enemy Colonies
Defeat the Ancient Guardians
Defeat the Legendary Pirates
Defeat the Shakturi
Destroy 1000 Enemy Civilian Ships and Bases
Destroy 10 SilverMists
Destroy 50 SilverMists
Destroy 100 SilverMists
Eliminate 5 Enemy Empires
Eliminate 10 Enemy Empires
Eliminate 5 Pirate Factions
Eliminate 10 Pirate Factions
Eliminate 20 Pirate Factions
Change Government to Way of the Ancients
Change Government to Way of Darkness
Join the Freedom Alliance
Join the Shakturi (Mutual Defense Pact)
Start 20 Wars
100 Successful Espionage and Sabotage Missions
1000 Successful Espionage and Sabotage Missions
Spend at least 90% of time at War
10 Successful Raids against enemy colonies and bases
50 Successful Raids against enemy colonies and bases
100 Successful Raids against enemy colonies and bases