Here's a summary from Wikipedia which I've shortened:
SPOILER
During their last dinner party together, the SEES members discover that they are trapped in their dorm, and that the day March 31 is repeating itself. Later, a large hole opens in the floor of the dorm, and SEES is attacked by Metis, an anti-Shadow weapon similar to Aigis. In the midst of fighting Metis to protect her friends, Aigis's Persona, Athena, transforms into Orpheus, the original Persona of the Protagonist. She also gains the Protagonist's Wild Card ability. Aigis is able to subdue Metis, whose actions were an attempt to end the time skip and save Aigis, who she calls her "sister".
Underneath the dorm is the Abyss of Time, the cause of the time skip. The Abyss contains seven doors, all leading multi-floor dungeons, similar in design to Tartarus. At the top of the seventh and final door, SEES fights a Shadow-like version of the Protagonist. After defeating it, each of them obtain a key. By combining the keys, they would be able to end the time skip and leave the dorm. However, Metis presents SEES with an alternative: they may also use the keys to travel back in time, to before the fight against Nyx and the death of the Protagonist, allowing them to prevent it.
Unable to agree on how to use the keys, the characters determine that they must fight each other to decide. Aigis and Metis claim all eight keys, which fuse into the Final Key. The group then discovers a new door in the Abyss of Time, which they use to travel to the moment the Protagonist sealed Nyx from the world.
Metis explains that the purpose of the seal created by the Protagonist was not to seal Nyx from humanity, but to prevent humanity from calling out to Nyx. However, the malice of the human race manifested in a monster called Erebus, which was able to break through the seal, causing the time skip. SEES fights and defeats Erebus.
After breaking the time skip and exiting through the front door of the dorm with the Final Key, Metis, Aigis, and the rest of SEES are summoned to the Velvet Room. There they learn that Metis is a manifestation of a part of Aigis's personality. Distraught over the death of the Protagonist, she no longer wanted to live like a human, and wished to return to being a machine. However, after being set free from the Abyss of Time, Aigis changes her mind, deciding to continue to attend school, something she had chosen not to do earlier.
Underneath the dorm is the Abyss of Time, the cause of the time skip. The Abyss contains seven doors, all leading multi-floor dungeons, similar in design to Tartarus. At the top of the seventh and final door, SEES fights a Shadow-like version of the Protagonist. After defeating it, each of them obtain a key. By combining the keys, they would be able to end the time skip and leave the dorm. However, Metis presents SEES with an alternative: they may also use the keys to travel back in time, to before the fight against Nyx and the death of the Protagonist, allowing them to prevent it.
Unable to agree on how to use the keys, the characters determine that they must fight each other to decide. Aigis and Metis claim all eight keys, which fuse into the Final Key. The group then discovers a new door in the Abyss of Time, which they use to travel to the moment the Protagonist sealed Nyx from the world.
Metis explains that the purpose of the seal created by the Protagonist was not to seal Nyx from humanity, but to prevent humanity from calling out to Nyx. However, the malice of the human race manifested in a monster called Erebus, which was able to break through the seal, causing the time skip. SEES fights and defeats Erebus.
After breaking the time skip and exiting through the front door of the dorm with the Final Key, Metis, Aigis, and the rest of SEES are summoned to the Velvet Room. There they learn that Metis is a manifestation of a part of Aigis's personality. Distraught over the death of the Protagonist, she no longer wanted to live like a human, and wished to return to being a machine. However, after being set free from the Abyss of Time, Aigis changes her mind, deciding to continue to attend school, something she had chosen not to do earlier.
