This is part of the story and therefore unmissable. The steps for this part of the story are:
Following on from Break and Enter, you will now have to find the Phoenix Mirror in your home. I first spoke with Ine-san at home and she informed me Fuku-san was looking for me. I went outside and found him at the tree near the dojo (he may be in the house or in the dojo depending on time of day) and experienced a cutscene. I then went into town to the antique store. After a cutscene, I was given a sword guard.
At this point, it could be useful to head to the Tomato Convenience store (2) to grab a torch and a light bulb. You will be entering a dark area, so it speeds up the next bit. Alternatively, you can get matches and candles from the shrine in your house, and use those. (I am unsure if the torch is essential or not. I had one, so used it immediately).
Head home, experiencing a cutscene and a fight on the way. Speak with Fuku-san outside your front door, then you will finish up in the house, go find Ine-san and speak with her. In the room next to the alter room, is a desk with a letter on it. In the drawer you will find a box containing a key.
Now head to the dojo and look at the box on the floor to the right of the 2 scrolls. Whilst looking at it, go into the menu with Triangle and select the Mysterious Key. This should unlock the box. Now look at the 2 scrolls on the wall and you should put each of them on the floor. In the left side mark on the wall, put the sword guard from your triangle menu. On the right side mark, activate it and you should push the sword in.
A door opens, you will go inside and down the ladder. Now activate the torch from your triangle menu and walk in. If you look at the light on the ceiling, you can put the bulb in from your menu. Then push the light switch. You can then put the torch away. Alternatively, there are candles around the room you can light.
On the left side of the room is a shelving unit. Next to this on the floor are scratch marks. Once you look at those, you can activate it to slide it. Then looking at the wall behind it, you see it is different. Look back at the door you came in and to the left of it you will find an axe you can use on the wall to break it and find the mirror, unlocking this trophy.
Make sure you do the following next or you could miss it (Make a save before hand. Read it can be buggy):