Here is the full list of all 41 Demon Gaze Global Edition trophies - there are 25 bronze, 12 silver, 3 gold and 1 platinum.
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Defeated the Demon of Time, Quasar!
Got the Big Muramasa
Got the Muramasa
Defeated the Destiny Demon, Aries!
Got the Ultimate Renter's Award
Defeated the Archangel of Darkness!
Became Friends with Pinay
Became Friends with Prometh
Get the Shield of the Three Treasures
Strengthened a Unique Item to Max
Got the Sword of the Three Treasures
Defeated the Darkness Demon, Pluto!
Won 1,000 Battles
Defeated the Light Demon, Uranus!
Killed 3,000 Monsters
Entered King's Eden
Defeated the Moon Demon, Luna!
Defeated Lord Shark
Defeated the Evil Demon, Astro!
Defeated the Beauty Demon, Venus!
Defeated the Lightning Demon, Jupiter!
Changed Your Looks
Entered Grimodar Castle
Got the Ring of the Three Treasures
Defeated the Midgard Heart
Defeated the Water Demon, Neptune!
Killed 1,000 Monsters
Entered Blue City
Defeated the Wind Demon, Hermes!
Got the Effect of Furniture
Defeated Midgardsormr
Activated a Gate Stone
Defeated the Fire Demon, Mars!
Strengthened a Normal Item to Max
Won 100 Battles
Defeated the Earth Demon, Chronos!
Rented a Room
Paid Rent for the First Time
Owed Rent Money
Defeated the Star Demon, Comet!