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