Madama Khepri, the Protector of Time, is a demoness with whom Rosa has a contract.
Like Madama Butterfly and Madama Styx, Madama Khepri physically resembles a cross between a human and an insect. In this case a scarab.
Book of Infernal Demons
"A goddess of Inferno who controls time and the sun. It is said that she can determine a person's fate by gazing upon the long shadow that forms between their body and the light extending from the land of the dead.
By binding a contract with Khepri and forfeiting their soul, one can gain an almost infinite knowledge of time and the secret technique to control it."
Madama Khepri aids Rosa in battle; the demoness' fists and feet emerge from Inferno whenever Rosa uses a Wicked Weave attack, and her shadow can be seen whenever Rosa is near a light source.
Madama Khepri is dark green in coloration; her wings and outfit sport gold decorations, and she wears a revealing dress, as well.
Madama Khepri's name is derived from that of an Egyptian deity who is closely affiliated with insects, namely the scarab beetle.
Concept artwork of Madama Khepri
Madama Khepri as she appears in the Book of Infernal Demons
Madama Khepri's shadow as it appears beneath Rosa
Madama Khepri's hand as it appears in the Records of Time
Madama Khepri's foot as it appears in the Records of Time
Madama Khepri is the only Infernal Demon to be associated with the sun.
Unlike Madama Butterfly and Madama Styx, Madama Khepri's body is never fully seen. In fact, if playing as Rosa in cutscenes and sequences where Bayonetta summons Madama Butterfly (such as in Chapter 4 where Bayonetta fights the Masked Lumen), Madama Khepri does not appear; instead, Madama Butterfly is summoned.  This is because Madama Khepri does not have a full model, only her arms and legs.