Both one of Her weaknesses and Her strengths is her beauty.
Persephone is a goddess out of Greek myth.
Goddesses do not know weakness. In listing a weakness, the label reveals more of the individual then that of a deity.
This Greek goddess did not have much time for "hobbies" given her duties as both Queen of the Underworld, Mistress of the Furies, and goddess of Spring.
Not that is known in mythology.
Nemesis is a goddess. No myth involving a particular weakness, either.
Persephone's mother was Demeter, the goddess of agriculture.
Hebe, the Greek goddess, has no weakness that are noted in myth.
Hades.
In ancient Greek myth, Eris is never mentioned having a weakness, nor engaging in a fight she loses.
Persephone, being a goddess, could change the color of her eyes at will.
She was Queen of the Underworld and goddess of Spring: Persephone's traits tied to these aspects of her being a Greek goddess - it also depends on the situation and myth.
Persephone was a goddess; they could usually do what they wanted to do without learning it, and when they wanted to do whatever it was, it was done.