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