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