Cassandra Cain is an odd case. She received plenty of emotional support and positive reinforcement from the man who raised her from birth to around age eight (who was also eventually revealed to be her biological father), however shooting her until she learned to get out of the way and preventing her from learning language so that segment of her brain would read bodies instead qualify as abuse under any definition imaginable.
Stephanie Brown's father, in addition to being a supervillain who tried to kill her with Black Mercy, would lock her in a closet when he was angry at her.
Batman himself sometimes dips into this, depending on the writer. All-Star Batman & Robin, the Boy Wonder is the worst offender (the goddamm Batman forces the 12-year-old Dick Grayson to live in the cave and eat rats), but it's sometimes seen in the regular universe as well. Bruce can go from the world's best father to the cruelest monster imaginable within 3 issues.
Damian Wayne is essentially at the centre of the world's most bizarre custody battle between two perfectionist control freaks. He was raised by his mother, Talia Al Ghul, for the first ten years of his life. Whilst she spoilt him rotten, she also trained him as an assassin. When he rejected her way of life in favour of following his father's ideals and Dick Grayson, she used his new spine to mind control him, disowned him, put a price on his head, and ultimately had him murdered by his own clone. He got better.
While Tim Drake's parents were generally just obscenely neglectful his father Jack is frequently emotionally abusive and manipulative, and the way Jack flipped out completely when Tim made a joke about Jack hitting him when Jack's new girlfriend was present suggested Jack had actually hit him before.
Honestly it'd be harder to name a member of the rogues gallery that wasn't a victim in at least one version of their origin story (fathers being the most common). Do keep in mind that many of these are prone to Multiple-Choice Past due to continuity reboots:
The Joker has made claims of having one or more abusive parents to his various psychiatrists before in pre-New 52 continuity, most notably when he corrupted Harley Quinn, but even he isn't sure if he's telling the truth or not when he does. In New 52 continuity, it's been implied he genuinely did have one, in the form of a highly abusive aunt (she starved him, beat him, and washed his face with bleach regularly)... who knows if that will or won't remain canon, though.
The retellings of Two-Face's (i.e. Harvey Dent's) origin have this present, largely being physical with an emotional element. The origins of the "Two-Face" persona come from a twisted game Dent's alcoholic father would play with him, based on a coin toss; heads, Dent's father would beat him senseless, tails, Dent would be off the hook. The catch was that the coin was a double-headed one, and Dent never won. The idealistic part that hoped the coin would land tails one day would go on to be Harvey, while the cynical part that knew it never would became Two-Face.
Riddler's father was so bad that he actually legally changed his name from Edward Nashton to Edward Nygma. Even when he wasn't beating the shit out of him, he verbally abused him by calling him a "moron" which is partially why he has such a need to prove his genius. This was also carried over to the Arkham games to the point of having a Freudian Slip during one confrontation with Batman.
Two for one deal with Scarecrow; there's the Post Crisis one where he was raised by a fanatically religious grandmother who would have crows attack him for the slightest perceived sin, and in the New 52 and Gotham his father would perform gruesome experiments on him or at least force him to participate.
Minor villain Humpty Dumpty had an abusive grandmother. His biography in Batman: Arkham Asylum states he eventually practiced his obsession with "fixing" on her, "dissasembling" and "reassembling" the old lady.
Batman: Black and White: In "Bent Twigs", an abusive father learns that his son has been looking after a cat on the roof of their apartment building and, in the course of the subsequent rant, throws the unfortunate cat off the building to teach his son a lesson. Cue the arrival of an extremely angry Batman, who was swinging past in time to see the whole thing (but not unfortunately in time to save the cat).
Knightfall featured Doctor Shondra Kinsolving, a physical therapist with some telepathic abilities who helped Jack Drake after he was tortured and also helped Bruce after his back was broken by Bane. When she is abducted by her foster brother Asp, Bruce's investigation into her past revealed that Shondra's adoptive father was a racist with a public appearance of being a benevolent figure of the community; her former foster mother speculates that he only adopted a black child so that he cold derive pleasure from beating something he believed was evil.
From Legends of the Dark Knight, we have Randolph Porter and General Slaycroft.
Randolph Porter was a brilliant pharmacologist and surgeon who deliberately put his daughter into a deathtrap Batman was not physically strong enough to free her from, and she drowned. This was part of ploy to get Batman addicted to strength-enhancing drugs (a predecessor to Venom) which also dimmed his intellect and put him under Porter's sway for some time. It should be noted that Porter himself was addicted to intellect-enhancing drugs which killed his empathy.
Porter's associate General Slaycroft employed him to create an army of drugged-up subservient super-soldiers using Slaycroft's own son (whom Slaycroft regarded as a sensitive wimp) as a template. This greatly modified the kid's personality, turning him from a nice kid into a violent thug who killed the girl he loved in a fit of rage. Slaycroft was also aware that the drugs he was having Porter pump into his son were greatly shortening his lifespan. He didn't care.
One of The Joker's "scar stories" in The Dark Knight has Joker claiming that he got at least one of the Glasgow Grin scars from his drunken father as a child, after said father stabbed his mother to death right in front of him. He later implies that this particular story is his actual origin ("You know, you remind me of my father. I hated my father!")
Joker (2019): In a flashback, it is shown that Penny Fleck's boyfriend used to severely beat her son Arthur, all the while she did nothing about it. Realizing this brings Arthur further into madness and it becomes a key factor of him becoming The Joker.
"Hidden Agenda" featured a student whose mother had unbelievably high standards for him. When he got a 2391 out of 2400 on the annual exam, 2nd best in the school, she told him flat out he was a horrendous failure ("That just makes you the winning loser") who would never get ahead in life. Any sympathy is lost, however, when he's revealed to be a rather psychotic leader of a gang of Jokerz. Then again, his mother may have caused his psychosis, as evidenced by the fact that many of his acts as gang leader are to try and get rid of the one person who is academically better than him.
Willie Watt consistently suffers ridicule from his father for being a "wimp" who can't physically stand up to the bullies at school. Then, Willie gets a hold of his father's construction golem, develops a psychic link to it, and uses it to trash a party after one more humiliation causes him to snap. When his father, tracking the golem's disappearance, finds Willy and berates him once again, Willy proceeds to turn the golem on him. Batman saves the day, but the end result shows that the father is still a major Jerkass.
Mr. Watt: Well, at least he ain't a wimp no more. (Batman gives him a disgusted glare before leaving)
In the next episode featuring Willie, it's shown that Willie is detained in a high security juvenile center and is in fact very muscular and aggressive (what his father always wanted him to be). The guard who escorts Terry tells him that many in fact fear Willie and says that not even his father has visited him and that Terry is his first visitor.
The King and Queen of the Royal Flush Gang also fit the bill. They're clearly more concerned about Ten pulling her weight in the gang above everything else, with King outright berating her and Queen emotionally manipulating her into staying. In their second appearance, they faked their own kidnapping just to see how far Melanie would go to prove her loyalty. To be fair though, Queen at least is willing to speak to Melanie using her real name, and in their third appearance, she's still upset about Melanie leaving for good. That said, King isn't any better towards Jack, backhanding Jack in their debut and final appearances for a smart-alack remark and mentioning Ten respectively. Their final appearance also has him leave Jack behind.
Derek Powers exiled his own son Paxton to do his grunt work and taught him to care about nothing but seizing power. The episode in which Paxton is introduced demonstrate the consequences of raising a son this way.
In Batman: The Animated Series, before he became Robin, Tim Drake's father worked for Two-Face and often left his son (who was under 13 years old) alone to fend for himself for long periods of time. When he double-crossed Two-Face, he abandoned his son to run away, only to be found killed outside of Gotham.
Doctor Psycho's teenage son Herman angrily lists off the things he did to make his life a living hell such as locking him in the basement, murdering his friends, and naming him Herman. However, the two of them make up after Psycho explains that he did it all in order to make him a better supervillain out of love.
The Joker, being The Joker, keeps his past a mystery but during a group therapy session at Arkham being asked about his family was enough to make him murder the psychologist working there before Harley. When Harley questions him on this, he steals Ivy's maid story above but replaces her plant with a ferret (much to Harley's annoyance after discovering this in the present day, as she had bought him ferret paraphernalia for years).
Kite Man's parents resent him for not being born with superpowers like them and talk down to him at every opportunity. He put up with their verbal abuse his whole life but finally learns to stand up for himself through Ivy's encouragement.
