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