Nemesis: Martian Manhunter
Other Major Foes: White Martians
Appearances: One mini-series/trade paperback
Powers: Telepathy, flight, shape-shifting, superhuman physique, and telekinetic/psionic pulse blasts. Possibly other common Martian abilities.
Cay'an is a Green Martian who survived the destruction of Mars and set about avenging her slain people. Cay'an specifically sought the culprit, Ma'alefa'ak, but chose to torment his brother J'Onn J'Onzz in his absence. Cay'an also persecutes and otherwise molests any White Martians she finds, and isn't especially kind to humans, either.
Win: Cabal (9-5)
Lose: Bel Juz (1/4); B'enn B'urnzz (4-5)
Nemesis: Green Lantern John Stewart
Other Major Foes: The Green Lantern Corps
Appearances: 100+ comics.
Powers: Super strength, speed, and endurance. She is an expert hand-to-hand combatant with an arsenal of weaponry, though she has favored an energy staff for most of her career. Fatality can fly via jet boots, wears bionic arms, and has her own spaceship. Fatality briefly wielded a Qwardian power ring, and is currently a Star Sapphire who can create light constructs at will through Zamaron technology.
Fatality is an alien born of royalty who was training with the Warlords of Okaara when her home planet of Xanshi was destroyed during the Cosmic Odyssey. She set about avenging her slain people, specifically targeting the Green Lantern whose hubris imperiled her world, John Stewart. In his absence, Fatality set her sights on any Green Lantern with the misfortune to cross her path, especially Kyle Rayner. After years as a murderous vigilante, Fatality's heart was touched by the Star Sapphires, and she gave up willful anger and fear as motivations in favor of love.
This was one of the most obvious match-ups, since both ladies are single-minded in avenging worlds destroyed through the peripheral involvement of the Manhunter from Mars. Both villainesses have held their own against noteworthy if not always capital "F" formidable heroes. Cay'an is the better schemer, but I'd give Fatality the advantage in a straightforward confrontation.