Rishia was a fallen noble, who even had to sell herself into slavery for the sake of money.
And the one who saved her from such despair was Itsuki. He became her goal. Her aspiration.
That’s why she can overcome the despair before her right now.
Though she did lose to it once, and jumped into the ocean.
You can also say that she had enough willpower to do such a thing.
There are plenty of things that humans can do only if they have the resolve to die.