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