Nemesis: Martian Manhunter
Other Major Foes: The JLA
Appearances: 15+ comics
Powers: Flight, shape-shifting, Laser Vision and other heightened ocular abilities, nigh-invulnerability, invisibility, intangibility, and superhuman strength/ speed/ physique/ senses/ reflexes/ endurance and sometimes telepathy.
Bio: Ma'alefa'ak is the evil twin brother of J'Onn J'Onzz, established from birth by his own mother as the darkness to the Martian Manhunter's light. Ma'alefa'ak killed and molested much of his extended family, including being credited with unleashing a plague that killed most of the inhabitants of Mars.
Win: Asmodel (13-6); Commander Blanx (5-2); Darkseid (?); Despero (9-7); Fernus (18-5); The Hyperclan (10-4); The Master Gardener (13-5)
Lose: Despero (?)
Other Major Foes: Lex Luthor, Superman Family
Appearances: 350+ comics, newspaper strips, animation, video games and live action television.
Powers: Flight, flame breath, vacuum breath, freeze vision and other bizarre ocular powers, invulnerability, and superhuman strength/ speed/ physique/ senses/ reflexes/ endurance.
Bio: Bizarro is a flawed duplicate of Superman whose power set works in a contrary version of the Man of Steel's. At various times, he has existed on a whole world of like creatures, or been a lonely creature with nothing like him in existence. Sometimes the product of science, other times magic, Bizarro is always an unstable, unpredictable, overwhelming force of the unnatural kind. Bizarro typically does not understand the difference between good and evil, is easily confused/confusing, and often actively attempts to do the opposite of whatever he interprets as Superman's actions.
Given Bizarro's tendencies, a team-up would be more likely than a brawl, but the reverse-Superman does seem to have a bit of a soft spot for life that Malefic would chafe against. Bizarro is problematic, but he/it does function within uncertain, garbled ethical parameters. Malefic has the raw power and lack of compunctions to take down Bizarro by any of the considerable means at his disposal, and I expect he could do so, as long as Bizarro doesn't have time to mount a response. Breathing fire and having most of the same powers as Malefic to a greater degree could make life very hard on a Martian psychopath.