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