Here is the full list of all 25 Unending Galaxy achievements.
Manage to survive the initial loading
Complete the tutorial
Complete the AI Core plotline
Build your first shipyard
Build your first military base
Destroy a pirate base
Kill a Swarm Queen
Colonize a sector
Build 10 battleships in a single game
Build 10 shipyards in a single game
Destroy 10 pirate bases in a single game
Complete a Relation mission
Complete a Pirate Base Destruction mission
Complete a Supply Delivery mission
Submit a Workshop item
Cause the Ceridans to invade
Declare war on another faction
Become allies with another faction
Stop clicking me, you creep!
Complete a Pirate Boss Destruction mission
Kill a Mynock hive
Complete a Swarm Hive Destruction mission
Complete a Factory Destruction mission for the Pirates
Control 40% of colonizable sectors
Let them fight for the map