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