Here is the full list of all 38 Sol Trader achievements.
Achieve a net worth of $5,000
Achieve a net worth of $10,000
Achieve a net worth of $50,000
Achieve a net worth of $250,000
Achieve a net worth of $1,000,000
Achieve a net worth of $5,000,000
Complete 1 mission
Complete 10 missions
Complete 25 missions
Complete 50 missions
Complete 100 missions
Convince someone to lend you a ship
Complete a mission to discover some gossip on someone else
Hire a ship
Hit your life goal
Complete a information-giving mission
Take a job in an organisation
Take a senior job in an organisation
Take a top job in an organisation
Kill another character
Take a loan
Pay off a loan
Take a job as a pirate
Discover a scandalous piece of information... and sell it for money to complete a mission
Become the owner of a Big Tiger class ship
Become the owner of a Cougar class ship
Become the owner of a Lynx class ship
Become the owner of an Ocelot class ship
Become the owner of a Tiger class ship
Sell a good to someone else
Upgrade your ship
Gain a visa to another part of the System
Visit 5 different cities
Visit 15 different cities
Visit all 25 cities
Buy your first ship
Hit your life goal within one in-game year of starting
Become the owner of a Puma class ship