How do you say peace be upon her soul in Hebrew?

There isn't an exact Hebrew translation for "soul". Also, if you're talking about a dead person, Hebrew speakers would say something completely different:

talking about a living person: sheh yihyeh la shalom (שיהיה לה שלום), "may she have peace".

talking about a dead person: zikhroná livrakhá (זכרונה לברכה), "may her memory be a blessing".