Trophies Glitch with story mode? pretty sure it something to do with Sleep mode.
I ran into this exact same issue too, was also suspecting sleep mode. After a certain point, loading screens wouldn't show up, and it'd just show the last image on screen until the next event was loaded.
However, I developed a worse issue.
I eventually beat every story mode by continually restarting the game and refusing to let it go to sleep. Both the game, and my trophy list agree, I've beat the story for all characters, except...
Someone please kill me.
I've been trying to replay every character again one by one but it's going about as well as you'd expect. I did some research and found someone posted that they replayed them all with no luck, reset their save data, and it still didn't trigger after beating everything a 3rd time.
I want to believe, so I'm not giving up. I'm replaying everyone again. I'll post if I get it to unlock.
Oh, also, I found another bug. I'm on the physical JP release version, and for those who don't know, the JP standard is O to advance and X to return to previous (see below)
Anyways, I happen to notice that the button prompts in the Art Gallery are displaying the wrong standard for JP. The Circle button still opens and the Cross button still closes, but the UI is incorrect. Also, the START button prompt is a little on the massive side.
Also, this might just be a me thing, but I played this game on both my JP Vita (NA account) and my NA PlayStationTV (JP account), and in both scenarios, the game defaulted the in-game language to, well, "default", which happens to be English.
Now, I don't have a JP system with a JP account on it, but I've covered both bases and I'm pretty sure that the game defaults to English on the JP cart. Can someone confirm this? Would be kinda shitty for JP players to be greeted to a game that doesn't actually default to Japanese.