Here is the full list of all 15 Amazing Discoveries In Outer Space trophies - there are 13 bronze, 1 silver and 1 gold.
Seen and done it all
Found 50% of the discoveries
Finished ODYSSEY
Finished ODYSSEY without taking shortcuts
Finished VOYAGE
Finished VOYAGE without taking shortcuts
Finished ENDEAVOUR
Found a secret solar system
Cracked open an asteroid to get the good stuff
Repaired a space probe and drained energy from it
Started a fashion trend
Defended yourself using a M.A.D.
Scanned a sun without taking damage
Discovered all life forms
Finished ODYSSEY in less than 20 game world minutes without using shortcuts