Here is the full list of all 21 Yu-Gi-Oh! Legacy of the Duelist achievements.
Win all Duelist Challenges
Unlock all avatars
Win an unranked multiplayer match (duel)
Win a ranked multiplayer match (duel)
Defeat ZEXAL Campaign
Defeat 5Ds Campaign
Defeat GX Campaign
Chain 100 times
Deal 50k in Reflective Damage
Deal 100k in Effect Damage
Defeat Classic Campaign
Deal 200k in Direct Damage
Create 5 decks
Create your first deck
Win a Battle Pack match (duel)
Perform a Xyz Summon
Perform a Synchro Summon
Perform a Pendulum Summon
Perform a Fusion Summon
Perform a Tribute Summon
Win a duel by having all Exodia cards in hand