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