Just going to leave this information regarding the "Cat Burglar" trophy here for anybody that needs it in the future. There is a lot of misinformation about this trophy out there including on this site's trophy guide. Not everyone has this issue but it's extremely frustrating when it happens to you. This trophy wasn't unlocking for me after feeding the cat and talking to Nozomi endlessly throughout the game. I understand that other people often have an issue with this trophy. I did a lot of reading online for tips about getting this trophy, however everyone seemed a little clueless about what actually triggers the cutscene you need to get this trophy. Turns out that on the day that you trigger the cutscene where Nozomi says that the cat is missing (the day after you show the phoenix mirror to Master Chen), there must be clear skies (it must not be raining or snowing) to get the cat spawned at the bottom of the stairs. This means that for getting this trophy you must not show the phoenix mirror to Master Chen on a day before it will rain or snow. To check that the weather will be ok the next day you can dial 177 on the phone to check the next day's weather. It may say that the day begins with clear skies and this is ok, you will have enough time to get to Nozomi before it snows or rains.
To recap: if you are having trouble with this trophy then play the game up to when you find the phoenix mirror but before you show it to Master Chen. Then dial 177 on the phone to check tomorrow's weather. If you are told that there is a part of tomorrow that is "fine" then show the phoenix mirror to Master Chen and after the cutscene you will wake up the next day. If not wait until the next day and check the weather (repeat until you are told that the weather is "fine" tomorrow). Walk up to Nozomi at the time of day where the weather is fine, talk to her and the cat will spawn under the stairs as it should.
Additionally, contrary to what almost everyone thinks and writes on trophy guides, you do not actually need to be feeding the cat regularly, in fact you do not need to feed it at all. However, you do need to talk to Nozomi a few times to trigger those cutscenes with her before you get to showing the phoenix mirror to Master Chen.
Hope this saves endless hours of research for other people online in the future.