Nemesis: Martian Manhunter
Other Major Foes: Project Cadmus, Harley Quinn, Dr. Trap
Appearances: 5+ comics
Powers: Telepathy, Telekinesis, Psionics, mind-control & psychic projection.
Bio: Bette Noir was a morbid genetic experiment contained by Project Cadmus until she discovered her ability to project an attractive image of herself across short distances. Bette lured telepaths into traps with her illusory form, then drained their psychic energy like a mental succubus. Bette's physical form was eventually murdered by Dr. Trap, but she lives on as a purely psychic entity, traveling from mind to mind.
Win: Bel Juz (8-4*); D'Kay (14-3); Doctor Samedi (14-3); Scorch (8-7*)
Lose: Despero (6-7); Professor Arnold Hugo (4-9)
*Denotes multi-participant match, rather that a duel.
Nemesis: Wonder Woman
Other Major Foes: Silver Swan, the Secret Six, Superboy, Superman
Appearances: 100+ comics and the DC Universe Online mmorpg.
Powers: Telepathy and vivid illusions.
Bio: Edgar Cizko was a disturbing, disgusting dwarf who hated women and used them as his unwilling mediums into manipulating the psychic plane.
Dr. Psycho is one of my favorite comic book villains and Wonder Woman foes, while Bette Noir is an Ostrander/Mandrake creation from their Martian Manhunter ongoing series that I've managed to avoid covering for six years and counting. That said, Psycho works because of his unique presentation and his being a mentalist who typically clashes with overwhelming physical forces. He brings telepathy to a fist fight, which shakes up the dynamics of his foils' stories (well, not Superman's, but definitely Wonder Woman's.) Curiously, the Alien Atlas didn't deal with many (any?) non-Martian/Saturnian psychics in his one ongoing, and that book did not shy away from the upper limits of J'Onn J'Onzz's considerable telepathic prowess. Bette Noir is a specialist, and while she has a lot in common with Dr. Psycho's sometimes partner Silver Swan, her powers set is more comparable but superior to Psycho's own. Though it pains me for once, I think the Vile Menagerie puts the little monster down.