Full list of all 28 No Man's Sky trophies - 10 bronze, 9 silver, 8 gold and 1 platinum.
The base game contains 23 trophies, and there is 1 DLC pack containing 5 trophies.
Platinum
Attain ‘Naturalist’ status in Planet Zoology Scanned
Attain 'Trailblazer' status in Space Exploration
Attain ‘Entrepreneur’ status in Most Units Accrued
Attain ‘Confused’ status in Words Collected
Attain ‘Known’ status in Alien Colonist Encounters
Attain ‘Novice’ status in Ships Destroyed
Attain ‘Archivist’ status in Planet Zoology Scanned
Attain 'Pioneer' status in Space Exploration
Attain ‘Trader’ status in Most Units Accrued
Attain ‘Interpreter’ status in Words Collected
Attain ‘Diplomat’ status in Alien Colonist Encounters
Attain ‘Notorious’ status in Ships Destroyed
Attain ‘Robust’ status in Extreme Survival
Attain ‘Nomad’ status in On-foot Exploration
Attain ‘Encyclopedia’ status in Planet Zoology Scanned
Attain ‘Discoverer’ status in Space Exploration
Attain ‘Magnate’ status in Most Units Accrued
Attain ‘Babelfish’ status in Words Collected
Attain ‘Ambassador’ status in Alien Colonist Encounters
Attain ‘Legend’ status in Ships Destroyed
Attain ‘Everlasting’ status in Extreme Survival
Attain ‘Adventurer’ status in On-foot Exploration
Claim a Base or Buy a Freighter
Build an Exocraft
Visit another Player's Base
Reach the Centre of the Galaxy in Survival Mode
Reach the Centre of the Galaxy in Permadeath Mode