Here is the full list of all 23 Cat Quest trophies - there are 7 bronze, 7 silver, 8 gold and 1 platinum.
MEOW!
Obtained 66 armor or weapons
Reached level 99
Cleared all 52 dungeons
Completed all 62 side quests
Completed the Main Quest
Defeated the Arcane Dragon
Located all monuments
Cleared 25 dungeons
Reached level 50
Defeated the Ice Dragon
Obtained all 7 skills
Obtained 30 armor or weapons
Defeated the Flame Dragon
Completed 30 side quests
Obtained 4 skills
Located half the monuments
Completed 6 side quests
Reached level 10
Cleared 5 dungeons
Obtained 3 armor or weapons
Obtained 2 skills
Located one monument