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