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