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