Walpurgis comes, and Madoka is the only one left to stop it. Homura says she shouldn't do it, as she's going to get herself killed, but Madoka says that this is the only road left for her now. She is still happy that she could save Homura from Izabel that day, and says that she will not let her's and Mami's feelings end in hypocrisy by turning into a witch.
She goes in, and defeats Walpurgis. Heavily weakened, she asks whether her life has really been an upstanding one, and drops dead. Homura comes on the scene later, overcome with grief, saying that her life means nothing without Madoka. Kyubey, hearing this suggests Homura make a contract to save Madoka's life. Despite knowing the fate of Magical Girls, Homura still decides to make a contract, and resets time.
Defeating Walpurgis is going to be much harder this time, because you'll only have Madoka to fight with. You should use all the extra stat points on her, and all the spell books as well. Spell books can be farmed on the floor before Walpurgis, from the Healer familiars.
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