Shakespeare shows the four lead female characters in the play as strong and determined women, but in the light of each one facing a challenging situation brought on by patriarchy. Hippolyta, the former Amazon queen captured by Theseus and engaged to marry him, accepts the situation outwardly graciously, though not with the same impatience to marry that he shows. He does not want to wait four days to marry; she thinks the time will past very quickly. She is the most cryptic of the women, as we do not get access to her thoughts.
Hermia is in the unfortunate situation of being in love with Lysander while her father wants her to marry Demetrius. Theseus backs Egeus, her father, despite Hermia's pleas that he see life through her eyes and let her choose her spouse. She therefore agrees to run away with Lysander through the forest and elope. She shows she is willing to challenge patriarchy's idea that she must mold herself to please her father.
Helena also is determined to have what she wants, which is Demetrius. Hers is a more destructive and unhealthy version of love, for she calls herself a "spaniel" and says that Demetrius can abuse her as long as she be near him. However, she knows her own desires and boldly follows Demetrius into the woods to try to woo him. Demetrius thinks he can get what he wants by allaying with patriarchal power.
Like Hermia, Titania stands up to patriarchy, refusing to give Oberon her ward, a young Indian boy whom she promised she would care for if his mother died. In weaving compelling pictures of their friendship, especially as the two of them watched the billowing sails of the ships at sea on Neptune, we can understand why Titania would stand up to her husband in wanting to honor the wishes of her friend.
In all four cases, women are shown as not having much power in patriarchal society. Hippolyta is being forced into a marriage against her will, and Hermia is expected to marry whomever who father wants, whether she likes it or not, or face harsh consequences, Helena is made abject in her quest for a man who does not want her, and Titania falls victim to Oberon's love potion, meant to force her to fall in love and thus be distracted from protecting the Indian boy. Yet three of the four are fighting back against circumstances, while Hippolyta is so self possessed it is hard to imagine she doesn't have a plan going forward. As is often the case with Shakespeare, he shows strong women working to get what they want despite the forces arrayed against them.