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