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