Meg Murry is the protagonist in A Wrinkle in Time by Madeleine L'Engle, and she experiences many conflicts throughout the novel.
The most significant earthly conflict Meg experiences is in school. She is exceptionally bright and does not fit in; she is an outcast among her peers and Meg often challenges authority and gets in trouble for it.
One other slight conflict is with Calvin O'Keefe, a boy who does seem to be anything like her but expresses his interest. Meg is conflicted about trusting this young man or not.
Her other-worldly conflict is much more serious, as she must fight the forces of evil (in the form of IT) to retrieve her father and save her brother, Charles-Wallace.
IT was the most horrible, the most repellent thing she had ever seen, far more nauseating then anything she had ever imagined with her conscious mind, or that had ever tormented her in her most terrible nightmares.
It is a costly battle and Meg suffers during the showdown; however, she is victorious because she fights with the help of others, though she must actually face her foe alone. In essence she (and her brother and Calvin) are the good which defeats the greatest evil.
Perhaps the biggest conflict Meg experiences is internal. When she goes back to Camazotz alone to rescue Charles Wallace, one of the "good witches" (Mrs. Which) tells Meg she has a weapon to fight IT but Meg must discover what it is on her own.
Love. That was what she had that IT did not have.
She wins her internal battle when she discovers that her greatest weapon is love.