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