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