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