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