Here is the full list of all 42 DEMON GAZE EXTRA achievements.
Defeated the Star Demon, Comet!
Defeated the Fire Demon, Mars!
Defeated the Earth Demon, Chronos!
Defeated the Wind Demon, Hermes!
Defeated the Water Demon, Neptune!
Defeated the Beauty Demon, Venus!
Defeated the Evil Demon, Astro!
Defeated the Lightning Demon, Jupiter!
Defeated the Light Demon, Uranus!
Defeated the Darkness Demon, Pluto!
Defeated the Moon Demon, Luna!
Defeated the Archangel of Darkness!
Defeated the Destiny Demon, Aries!
Defeated the Demon of Time, Quasar!
Entered Blue City
Entered Grimodar Castle
Entered King's Eden
Activated a Gate Stone
Rented a Room
Became Friends with Pinay
Became Friends with Prometh
Defeated Lord Shark
Defeated Midgardsormr
Defeated the Midgard Head
Got the Ring of the Three Treasures
Got the Sword of the Three Treasures
Get the Shield of the Three Treasures
Paid Rent for the First Time
Got the Ultimate Renter's Award
Owed Rent Money
Strengthened a Normal Item to Max
Strengthened a Unique Item to Max
Won 100 Battles
Won 1,000 Battles
Killed 1,000 Monsters
Kill 3,000 Monsters
Got the Muramasa
Got the Big Muramasa
Got the Effect of Furniture
Changed Your Looks
You added the special class as party members.
You synthesized some gear.