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