Here is the full list of all 15 NekoBuro CatsBlock trophies - there are 13 bronze, 1 silver and 1 gold.
Tried all the toy with cats.
Clear Stage 5.
Clear Stage 4.
Clear Stage 3
Get an Mr.Researcher doll.
Clear Stage 2
Play with cats for the first time
Clear Stage 1
Get 40000 score in Survive Mode.
Change the furniture
Getting a chain combo.
Stage 1-1 cleared
Get SS medal for every quest.
Get 200000 score in Survive Mode.
Get all furniture.