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