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
Create 5 decks
Create your first deck
Defeat GX Campaign
Unlock all avatars
Chain 100 times
Defeat ZEXAL Campaign
Deal 50k in Reflective Damage
Deal 100k in Effect Damage
Defeat 5Ds Campaign
Perform a Pendulum Summon
Perform a Xyz Summon
Perform a Synchro Summon
Defeat Classic Campaign
Win a duel by having all Exodia cards in hand
Deal 200k in Direct Damage
Perform a Fusion Summon
Perform a Tribute Summon