I think your girlfriend might have seen a few episodes of Sailor Moon's 5th and last season, "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, 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 cristals" parts of your description.

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

I think your girlfriend might have seen a few episodes of Sailor Moon's 5th and last season, "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, 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.