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