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