Here is the full list of all 21 Yu-Gi-Oh! Legacy of the Duelist achievements worth 1,000 gamerscore.
Performed an Xyz Summon
Won an unranked multiplayer match (duel)
Created 5 decks
Performed a Pendulum Summon
Performed a Synchro Summon
Dealt 200k in Direct Damage
Defeated Classic Campaign
Created your first deck
Performed a Fusion Summon
Performed a Tribute Summon
Won a duel by having all Exodia cards in hand
Defeat GX Campaign
Defeat 5Ds Campaign
Defeat ZEXAL Campaign
Win a ranked multiplayer match (duel)
Win a Battle Pack match (duel)
Unlock all avatars
Win all Duelist Challenges
Deal 100k in Effect Damage
Deal 50k in Reflective Damage
Chain 100 times