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