Below is the complete list of of all 23 trophies for No Man's Sky. I will elaborate further on the requirements as soon as I unlock these trophies myself.
Trophy Name: Total Perspective Vortex
Trophy Type: Platinum
Description: Obtain all other trophies.
Trophy Name: A Scanner Darkly
Trophy Type: Bronze
Description: Attain 'Naturalist' status in Uploaded Discoveries. Or catalog every creature on one planet.
Trophy Name: The Stars, Like Dust
Trophy Type: Bronze
Description: Attain 'Trailblazer' status in Space Exploration. Or warp a total of three times.
Trophy Name: Foundation
Trophy Type: Bronze
Description: Attain ‘Entrepreneur’ status in Most Units Accrued. Or have a total of 150,000 units in your possession at once.
Trophy Name: Babel-17
Trophy Type: Bronze
Description: Attain ‘Confused’ status in Words Collected. Or learn 10 alien words.
Trophy Name: Contact
Trophy Type: Bronze
Description: Attain ‘Known’ status in Alien Colonist Encounters. Or meet two aliens.
Trophy Name: Use of Weapons
Trophy Type: Bronze
Description: Attain ‘Novice’ status in Ships Destroyed. Or successfully destroy one starship.
Trophy Name: The Star Beast
Trophy Type: Silver
Description: Attain ‘Archivist’ status in Uploaded Discoveries. Or catalog every creature on 7 planets.
Trophy Name: The Longest Voyage
Trophy Type: Silver
Description: Attain 'Pioneer' status in Space Exploration. Or warp a total of 30 times.
Trophy Name: The Space Merchants
Trophy Type: Silver
Description: Attain ‘Trader’ status in Most Units Accrued. Or have a total of 1,000,000 units in your possession at once.
Trophy Name: The Languages of Pao
Trophy Type: Silver
Description: Attain ‘Interpreter’ status in Words Collected. Or learn 50 alien words.
Trophy Name: Who Goes There?
Trophy Type: Silver
Description: Attain ‘Diplomat’ status in Alien Colonist Encounters. Or meet 20 aliens.
Trophy Name: Pattern for Conquest
Trophy Type: Silver
Description: Attain ‘Notorious’ status in Ships Destroyed. Or successfully destroy 50 starships.
Trophy Name: Stranger in a Strange Land
Trophy Type: Silver
Description: Attain 'Robust' status in Longest Lifespan. Or survive 20.0 sols under extreme weather conditions without dying. A sol is equivalent to one in-game day, or about 15 minutes in real world time. This will be different for each planet, and you have to be wandering about in the open for the time to count.
Trophy Name: Symphony For A Lost Traveler
Trophy Type: Silver
Description: Attain ‘Nomad’ status in On-foot Exploration. Or travel/walk a total of 40,000 steps (40,000 miles).
Trophy Name: Galapagos
Trophy Type: Gold
Description: Attain ‘Encyclopedia’ status in Uploaded Discoveries. Or catalog every creature on 10 planets.
Trophy Name: A Space Odyssey
Trophy Type: Gold
Description: Attain ‘Discoverer’ status in Space Exploration. Or warp a total of 60 times.
Trophy Name: The Diamond Age
Trophy Type: Gold
Description: Attain ‘Magnate’ status in Most Units Accrued. Or have a total of 2,000,000 units in your possession at once.
Trophy Name: Citizen of the Galaxy
Trophy Type: Gold
Description: Attain ‘Babelfish’ status in Words Collected. Or learn 150 alien words.
Trophy Name: What Mad Universe
Trophy Type: Gold
Description: Attain ‘Ambassador’ status in Alien Colonist Encounters. Or meet 40 aliens.
Trophy Name: The Forever War
Trophy Type: Gold
Description: Attain ‘Legend’ status in Ships Destroyed. Or successfully destroy 80 starships.
Trophy Name: The Sentinel
Trophy Type: Gold
Description: Attain ‘Everlasting’ status in Longest Lifespan. Or survive 32.0 sols under extreme weather conditions without dying. A sol is equivalent to one in-game day, or about 15 minutes in real world time. This will be different for each planet, and you have to be wandering about in the open for the time to count.
Trophy Name: Have Spacesuit - Will Travel
Trophy Type: Gold
Description: Attain ‘Adventurer’ status in On-foot Exploration. Or travel/walk a total of 100,000 steps (100,000 miles).