Here is the full list of all 24 Reassembly achievements.
Destroy the largest crystalite ship
Explore all sectors in a galaxy
Destroy the crescent ship
Unlock all 7 factions
Die 100 times
Destroy 10 agents
Destroy 70,000P of ships
Build a ship with exactly 8000P
Acquire 10,000 C
Destroy 50,000P of ships
Explore 1000 Sectors
Activated 10 Stations
Destroy 30,000P of ships
Transfer 10,000 R to allies
Destroy 10,000P of ships
Destroy an agent
Activate all stations in a galaxy
Conquer all sectors in a galaxy
Explore 10,000 Sectors
Spawn 100 ships
Destroy 50 Agents
Travel through 1 wormhole
Travel through 10 wormholes
Acquire 100,000C