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