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