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