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