Here is the full list of all 46 Natural Doctrine trophies - there are 33 bronze, 9 silver, 3 gold and 1 platinum.
Earned every other trophy.
Saved Vasily.
Won a cooperative multiplayer match.
Found Vasily's ring.
Won 100 times.
Reached A rank.
Defeated a higher ranked player than you.
Earned 300 cards.
Obtained a card with a maximum size of 4.
Earned 50 cards.
Increased your multiplayer rank for the first time.
Won a competitive multiplayer match.
Created a deck of rating A or higher.
Obtained a truly superlative card.
Obtained 5 cards.
Switched out a card in a registered multiplayer deck.
Cleared the game without losing a single ally.
Defeated the gorian queen.
Stepped foot in the lair of the gorians.
Entered the fortress of Feste.
Linked with all 9 allies.
Ingbert joined the party.
Defeated a gorian dreadnought.
Gomori joined the party.
Defeated a gorian sentry.
Encounter the ancient dragon Onatu, secluded deep within the Sacred Mountain.
Erna joined the party.
Defeated a gorian ultron.
Borrowed a rare treasure from the kingdom of the lizardfolk.
Met Gomorrah, the Undying King.
Defeated the Undying King that reigned over the abandoned city of Sodom.
Defeated the minotaur.
Defeated Tatyana's parents.
Defeated 100 goblins.
Mel and her iron giant joined the party.
Zekelinde left the party, and joined up once again...
Tatyana joined the party.
Met Aslan, the Lion of Legend.
Collected a total of 10g of Pluton.
Vasily has left the party...
Used 'Pluton Arrow' for the first time.
Nebula joined the party.
Switched equipment during battle.
Defeated an enemy with return fire.
Signed a contract with Anka.
Defeated an enemy who had the next Initiative, leading to consecutive Initiatives.