My Sister Will Not Become a Magical Girl.

The manga's story centers on Akuto and his magical girl older sister Shiny, who fights a mysterious monster called "Acrylamide" that threatens the human world, after a meteorite crash. Akuto supports his sister's efforts as a magical girl, but then she commits suicide after defeating an Acrylamide. Akuto goes back in time before his sister becomes a magical girl and tries to stop her from committing suicide.

(Source: ANN)