I think your girlfriend might have seen a few episodes of Sailor Moon's 5th and last season, [_"Sailor Moon Sailor Stars"_](https://en.wikipedia.org/wiki/Sailor_Moon_Sailor_Stars).

The series originally aired in Japan from 1996 to 1997, so she could have seen a later rerun.

The *"main character"* your friend remembers could be [Sailor Galaxia](https://en.wikipedia.org/wiki/Shadow_Galactica#Sailor_Galaxia), actually the main villain of the season, whose backstory is shown as a flashback in one of the last episodes (if I remember correctly) and matches the *"going mad"* and *"looking for crystals"* parts of your description.

Sailor Galaxia, however, does not match the _"she will be born as a baby in each world"_ part.