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