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