I'm going to guilt trip my mentally unstable friend into valuing her own life
That is a weird way to do that. What is the plan?
I'll tell her how much her death would hurt me.
I'm not sure making her feel guilty will stop her from taking her life.
It's okay, she will learn a valuable lesson that whatever I say she'll listen to it.
She needs real help not a guilt trip. If you value her you would help her find a therapist or some sort of counseling.