Here is the full list of all 39 The Long Journey Home trophies - there are 22 bronze, 12 silver, 4 gold and 1 platinum.
Won all available trophies and contests in the galaxy
Brought the Daedalus-7 back home
Made it back home in Rogue Mode
Brought your whole crew back home
Brought the Mizzurani plague back to Earth
Explode during an uncontrolled orbit around a sun
Dared take a trip through a black hole
Visited and escaped one of the galaxy's most dangerous planets
Collected and kept 5 alien relics
Created a wormhole
Deployed an illegal gate hacking device
Brought at least 15 souvenirs back to Earth in one mission
Encountered all alien races at least once
Sold Earth to the Entrope for harvesting
Made enemies of everyone in the galaxy
YOU KNOW WHAT YOU DID
Made 999 credits in a single trade
Visited at least one ruin from every ancient civilisation
Failed before even getting out of Sol
Whatever you were thinking - no!
Left the Final Gate open
Destroyed the Final Gate
Double-checked the moon landings weren't a hoax
Discovered a distant piece of Earth history
Docked at a Raxact Black Market
Retrieved a legendary treasure
Exposed a galactic conspiracy
Won a round of Jassikan's Teeth
Helped the Cueddhaest ascend to the Nextplane
Accessed the Entrope database
Helped spark the Wolphax Rebellion
Won the Wolphax Grand Tournament
Discovered a cure for Kirsten's cancer
Defeated an ancient galactic evil
Discovered a stowaway before they were caught or fled
Became allied with the Raxact Horde
Repaid a gambler's debt in full
Let Squire Temrach have his victory
Ejected desperate alien refugees into space