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