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