Magia Record Story Otsukimi is After an Elegant Tea Party
The following is a summary posted on 4chan's /pmmm/ general.
Originally, only Hotori Yuuki is a magical girl and a Black Feather. Her sister, Rion Yuuki, is neither. During their tea party at Mizuna, Hattori found a witch and decides to defeat her because of her sense of justice.
Alas, the witch has became very powerful thanks to the negative emotions in Kamihama which is recovering from a terrible disaster, and Hotori is overwhelmed. The odds are against her since Rion is also caught in the barrier.
A random white feather tells a white lie which allowed the girls to retreat, but she is easily killed by the witch. It also destroys the old school compound, killing Hotori who protected her sister from the falling debris.
Thus, Rion contracts with the Kyubey who is stuck inside the witch's barrier (it entered when Eve was down, but become stuck when the small Kyubey sacrificed himself and reinstalled the barrier).
Rion's wish is to undo the tragedy. She has enough causality to create a new timeline to overwrite the old one, but it is not enough to completely cover up the event. Thus, the destruction is delayed, and killing the witch is a necessity.
Yukika's wish turns her into a trouble magnet and she is thus dragged into this situation. While she is able to let the normal people hold their party elsewhere, she is not strong enough to defeat the powerful witch. History repeats itself as she tells a white lie like the White Feather and lets the twins escape.
She has no regrets helping others in need, though she is frustrated and upset that she is unable to fulfill the White Feather's last wish which is to defeat the witch, and wasted Kyubey's sacrifice since it helped tank an attack for her.
She fought bravely, but is eventually overwhelmed, coughing out blood and not. However, her emotions exploded and her doppel finished off the witch.
In the end, she is able to see the moon with the council members of the two schools, and the twins grew closer to her even though they know now that she is not their savior.
Yukika seeks out Kyubey from the outside and is dismayed to know that even it did not know what happened to the Kyubey from the barrier other than it is dead. Kyubey explains that they will stop conducting experiments in Kamihama since there is no way to know what happens, and Yukika is now the only person to remember the White Feather and that Kyubey's sacrifice.
She admits that knowing the other side of the world, while exciting, is not what she expected.
It is amusing to note that Kyubey sees the doppel system as weaponizing the taint from Soul Gems. This, and the fact that Yukika's innate makes her more powerful when the odds are against her is why she was able to win.