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