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