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