One can relate it to fetishism, the cat becoming the substitute for the loss of the object. Indeed catwomans latex bodysuit and whip is archetypal fetishistic attire. Possessing a cat-like identity replaces her need to replace the phallus, indeed her strength and will, suggest she is in possession of the phallus, or at least believes this to be so. A shamanic interpretation of catwoman’s experience would be very different, although Freud attempted to explain shamanic experience in a purely material manner. Indeed Freud is quoted in his work on fetishism that; ‘substitutes are with some justice likened to the fetishes in which the savages believe that their gods are embodied’.
Even the characters that are not associated with an animal identity display particularly Dionysian traits, being instinctual and spontaneous, they are insane in the eyes of society. The Joker who constantly makes a joke out of everything and The Riddler with his symbol the question mark, who constantly questions the rules and values of the Apollonian ruling order.
Batman, the dark night, seems to have a constant battle within his own psyche as much as with the villains. His animal nature providing his crime fighting powers, but also his potential downfall. Catwoman often tempts him into her counter cultural lifestyle but in the end he manages to morally conquer this temptation and protect the values of industrial society.