Dream Hunter Rem (1985)

In this world, demons try to steal the life force of humans by invading their dreams. "Dream Guardians" are seemingly ordinary humans who hunt down the demons to defend humanity. The psychic girl Rem Ayanokoji is the latest descendant in a line of Dream Guardians. She is capable of entering the dreams of sleeping people to face the demons. She earns a living as a private detective, though she specializes in investigating supernatural cases. Her pet cat Alpha and pet dog Beta transform into more powerful forms to assist her in combat. Rem has no known living family members, but she has a mentor-like figure in the person of the ascetic monk Enko who uses his martial arts training and his faith-based abilities to help her cause.