In a nut shell, Sayuri has been in a dream the entire time. She fell into a coma at the church in the very begining, and everything in the game, other than the squad and a certain lady named Nene are all fabrications. Sumire and Nene reveal that the Shirasagi family was cursed since the original clan head Yurika(who happens to bear a strong resemblance in terms of appearance to Sayrui) , who bears a curse of short life span that affects the entire family, thus Sayuri is described by Sumire as always sickly and apparently the sisters lost their mother to the curse as well. Nene on the other hand, was a friend of Yurika, who was cursed with long life and has been around for centuries. When you reach the inner most floors of the dungeon, Sumire would urge Sayuri not to proceed any further, as Sayuri is content and helathy in the dream world. If she chanllenges the curse and fails, she will die in the real world. The squad(save Sumire, she was the one who employs the squad's help) on the other hand enter Sayuri's dream to help her out, but because of the strange nature of the dream world they lost their Persona and have no recollection of their original purpose.
To get the true ending you need to complete the optional dungeon(the entrance is a diamond with rainbow/transparent color), defeating all 6 bosses within and proceed to defeat the final boss. The normal/bad ending is simply defeating the final boss. True ending has a different theme than the normal/bad ending.
In the true ending, Nene reveals the optional bosses(who are all bosses from the previous game) is meant to test their mettle. With her assisstance the squad defated Yurika who's the source of the curse, freeing Yurika. Yurika saids she no longer has a body and thus decided to slumber within Sayuri's mind, assuring Sayuri that she would only very rarely wakes up and things should be fine. With that done Sayuri wakes up in the real world, tended by Retina. She graduated from her current school and is now in another school(could be just high school, but the wording is very vague), she visits the squad who are now in charge of the student council. With them and the Nene lady, they gather at the top floor and reminisce their friendship. Sayuri thanks each and everyone of them by calling them in their first names. Sayuri contemplated all the hardships she endured, but is happy that now she has a future, her family and friends, and it ends with her screams into the air "it was really fun!".
The normal/bad ending is very similar to the true ending, it also comes down to Sayuri visiting the squad at the top floor of the school, she seems happy that her friends are with her but she's affected by something and appears unwell, the game ends with a sudden black screen.
