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