Here is the full list of all 37 Rebel Galaxy achievements. It takes around 50-60 hours to unlock all of the achievements on Windows.
Become neutral to pirate factions
Break 1 blockade
Complete the main campaign
Find a Progenitor Shard
Reach rank 5 in any Guild
Complete 50 missions from the mission board
Rescue 20 merchants
Reach a Net Worth of 5 Million Credits
Gather 200 objects with a tractor beam
Salvage 50 Containers
Join the Merchant's Guild
Find an Antimatter Speck
Become friendly to the Militia
Hire a mercenary
Destroy 100 Capital-Class Craft
Destroy 250 Fighter-Class Craft
Join the Mercenaries' Guild
Trade with a Merchant while in flight
Jump out of the first solar system
Purchase a new ship
Collect 10 bounties
Woke Trell
Kill 1 Pirate Lord
Hack 10 transponders successfully
Destroy 2,500 Fighter-Class Craft
Destroy 1,000 Capital-Class Craft
Reach a Net Worth of 50 Million Credits
Shoot down 500 torpedoes
Pirate a merchant
Mine 50 asteroids using a Fault Tracker
Collect 100 bounties
Kill 20 Pirate Lords
Successfully bribe a Militia official
Find the Face of Gozu
Break 10 blockades
Purchase a Destroyer-class ship
Purchase a Dreadnaught-class ship