Here is the full list of all 12 Yu-Gi-Oh! Millennium Duels trophies - there are 7 bronze, 4 silver and 1 gold.
Complete Expert Mode.
Inflict at least 1,000,001 damage.
Win 15 ranked Matches.
Play 30 Multiplayer Duels.
Complete Yu-Gi-Oh! 5D's and ZEXAL series.
Complete Yu-Gi-Oh! and GX series.
Complete your first series.
Win a Duel and earn a second copy of a card.
Reach the top of the first Duel ladder.
Use a signature creature against their owner.
Win a Duel using a custom Deck Recipe.
Complete your first Duel.