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