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