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