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