Bruce: Joker (any other answer is wrong)
Dick: should be Deathstroke, but DC seems determined to pimp Slade out to every other hero in the DCU. Midnighter might be the current one.
Barbara: James Jr, God help her. Harley Quinn was arguably hers in the DCAU, and I think that would be better.
Tim: Probably that loser King Snake and other crappy villains from his 90s series.
Cass: Cain
Jason: Crowbars and his feelings of crippling inadequacy
Steph: Cluemaster
Damian: Talia?
Batman- Arkham Asylum
Nightwing-Deathstroke
Red Hood-Joker
Robin(Tim)-King Snake,the General, Anarky
Azreal-The System
The Dark Knight------>The Clown Prince
Grayson---------------> Jason
Damian--------------->Bane
Tim Drake------------>Scarface
Huntress-------------->Talia
Batgirl---------------->Catwoman
Jason X
Jason Todd is complex, since he's both Robin and the Red Hood, so I'd probably pit him against Zsasz, since they both capture the 'double-edged sword' of Gotham City.
Jason Todd
jt.jpg
Bruce - Joker
Dick - Deathstroke
Otherwise, I'm not really sure there are far too many worthy contenders.
Batman vs. Riddler. Batman has so many villains who are would-be arch, but Riddler's the only one who's straight up traditional Jim Moriarty (in spite of Joker's boasts).
Grayson vs. The Clock & Crazy Quilt! Or M.A.Z.E.!
Catwoman vs. ... it's hard not to agree with Black Mask, I guess. I thought Sylvia Sinclair was being totally groomed for it. You'd think it'd be a rival thief or a "thief-stopper".
Batgirl vs. Duela Dent. Straight outta Batman Family.
Red Hood vs. Oh Felipe Garzonas to be sure. He needs to haunt Jason ASAP, somehow. Him or his crooked dad or secret brother or somebody.
Tim Drake vs. Anarky. No matter the identity, Anarky is the perfect blend of physical threat and computer-based threat for Tim.
Cass? No clue. I mean her parents are her nemeses. And Mad Dog. And everyone. Kitty Kitumba, right?
Steph? Needs a proper rival for sure. An actual female archnemesis that has nothing to do with leagues or assassins or overly cluttered bat-baggage. Much as I love the BQM run, she was handling a lot of Bat-villains, only the Reapers were really fresh faces, but they weren't really nemesis material.
Damian ... hmm. I mean The Heretic seems pretty obvious but then his personal growth in the first issue of the "Superpower" arc seemed to put that behind him, right?
Retro315 no more. Anonymity is so 2005.
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