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