Shiva is a boss in Final Fantasy IV -Interlude-. She is fought in the Tower of Babil as part of a gauntlet of bosses leading up to the final boss. Edge can throw Flame Swords and Flame Lances at her or use Flame while Palom uses Firaga, and Cecil attacks with the Flame Sword.
Shiva (also spelled Śiva) is a Hindu god. The Hindu Shiva once saved the world by consuming poison, giving him blue skin around the area of the neck and throat. Shiva is a male god, but can merge with his consort Parvati to become Ardhanari, an androgynous Hindu god of duality. Shiva is the god of destruction along with Vishnu, who is the god of preservation, and Brahma, the god of creation. Together they are the three principle deities of the Trimurti (Hindu Triad). It is believed he periodically destroys the world, then recreates it.
Shiva has different human forms, males and females. When he was in his avatar form, he spent most of his times in the Himalayan snow mountain. Shiva in the Final Fantasy series is likely inspired by one of his female avatars.