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