Here is the full list of all 25 Yu-Gi-Oh! Legacy of the Duelist: Link Evolution trophies - there are 9 bronze, 8 silver, 7 gold and 1 platinum.
Defeat Yu-Gi-Oh! 5D's Campaign
Chain 100 times
Defeat Yu-Gi-Oh! ZEXAL Campaign
Defeat Yu-Gi-Oh! GX Campaign
Defeat Yu-Gi-Oh! Campaign
Create 5 decks
Win a duel by having all Exodia cards in hand
Perform an Xyz Summon
Win a Battle Pack match (duel)
Win a ranked multiplayer match (duel)
Win an unranked multiplayer match (duel)
Perform a Link Summon
Deal 200k Damage with Attacking Monsters
Perform a Synchro Summon
Perform a Tribute Summon
Perform a Fusion Summon
Create your first deck
Unlock every trophy in Yu-Gi-Oh! Legacy of the Duelist : Link Evolution
Defeat Yu-Gi-Oh! ARC-V Campaign
Defeat Yu-Gi-Oh! VRAINS Campaign
Perform a Pendulum Summon
Unlock all avatars
Win All Duelist Challenges
Deal 100k in Effect Damage
Deal 50k Damage with Defending Monsters