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