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
Cleared all 52 dungeons
Completed all 62 side quests
Completed the Main Quest
Obtained all 7 skills
Located all monuments
Cleared 25 dungeons
Completed 30 side quests
Reached level 50
Obtained 30 armor or weapons
Defeated the Arcane Dragon
Located half the monuments
Defeated the Ice Dragon
Obtained 4 skills
Defeated the Flame Dragon
Completed 6 side quests
Located one monument
Cleared 5 dungeons
Obtained 3 armor or weapons
Reached level 10
Obtained 2 skills