Here is the full list of all 24 Yu-Gi-Oh Legacy of the Duelist : Link Evolution achievements.
Perform a Fusion Summon
Win a duel by having all Exodia cards in hand
Perform a Tribute Summon
Defeat Yu-Gi-Oh! Campaign
Defeat Yu-Gi-Oh! GX Campaign
Defeat Yu-Gi-Oh! 5D's Campaign
Defeat Yu-Gi-Oh! ZEXAL Campaign
Perform an Xyz Summon
Perform a Synchro Summon
Perform a Pendulum Summon
Win an unranked multiplayer match (duel)
Win a ranked multiplayer match (duel)
Win a Battle Pack match (duel)
Unlock all avatars
Win All Duelist Challenges
Deal 200k Damage with Attacking Monsters
Deal 100k in Effect Damage
Deal 50k Damage with Defending Monsters
Chain 100 times
Create your first deck
Create 5 decks
Defeat Yu-Gi-Oh! ARC-V Campaign
Defeat Yu-Gi-Oh! VRAINS Campaign
Perform a Link Summon