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