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Nightmare Fuel: Batman Beyond
Blight nicely sets the Nightmare Fuel tone for the series right from the early going.
There's also what his chemical does. Probably due to censors, we don't actually SEE what happens to a human or an animal, but that arguably makes it worse given what we see it does to plants, and Derek's comment, depending on whether or not you think he was being literal or metaphorical, implies humans hit with it turn to dust if not treated.
Earthmover. Essentially a motionless, decaying corpse half-melted into the surrounding earth - except for the glowing green eyes. Seriously creepy even for this series, especially since his character model was more detailed than anyone else's.
In "Lost Soul," the final fate of Robert Vance. Whether he was the real deal or just a deluded, rogue program that thought he was Robert Vance, and regardless of the horror he was going to subject his grandson to note downloading his consciousness into Bobby's body, thus "erasing" Bobby; this feat would actually come to pass in "Out of the Past" with Ra's al Ghul and his daughter Talia (which is Nightmare Fuel in and of itself), seeing (and hearing) the man mentally regress to infancy and cry out for his mother and father as his data is deleted for good is cringe-worthy.
Robert Vance: "Five hundred megs! A thousand kilobytes! Pi r squared! Two plus two equals four!" (voice then reverts to that of a child, and then becomes baby talk) "Me first! I wanna play! One potato... two potato... Mama! Papa!... Mama!"
There's also the moment when Vance's program manages to get into the Batsuit. He realizes that Terry is nothing more than a hindrance, so he decides to get rid of him... by drowning Terry. The way that Terry fights the suit as it walks into the ocean is incredibly agonizing to watch. Sure, Bruce realizes what's going on and uses the failsafe "get the suit's joints to lock up" thing, but that only happens once Terry is neck-deep in the water already. He's stuck there, trying to stay upright and alive as he gets hit by wave after wave until Bruce finally comes to get him.
"Where will I be?" is answered with a deadpan, "Wherever deleted progams go." Robert Vance views his son as a program to be erased and replaced with himself.
Particularly chilling how, after injecting Terry with the splicing stuff, the doctor calmly tells him, "You're welcome to your opinions, while you're still human enough to have them."
Dr. Cuvier's final transformation. He starts off injecting DNA into himself to become a chimera. Terry then starts pumping random serums into him, causing him to turn into a mass of sinew and bile. See for yourself.◊
The flashback to Stalker's back surgery in "Bloodsport." It's made very clear that for whatever reason, the surgeons didn't want to put him under when replacing his spinal chord.
The Stalker was supposedly killed when he was run over by a train. Why didn't he leap out of the way? He hallucinated and thought it was a panther. In fact, the Panther that mauled him in the first place.
The subjugation the kids go through in "Last Resort." Children are brainwashed Big Brother-style, denied food, sleep, or even contact with the outside world until they break.
Inque's first serious attempt at killing Batman. She crams herself down his throat! Sure, Bruce and his fire hose come to the rescue, but that's got to be a pretty unsettling way to go...
How about what she does to Aaron Herbst, that poor guy who helps her get her humanity back in her second appearance?
In Return of the Joker, Terry returning to the Batcave to find it vandalized, and Bruce lying on the floor, dosed by Joker venom, barely able to move or speak without succumbing to the venom and nearly laughing himself to death. It had to be a bit of an in-universe example as well, since the scene with the vandalism directly recalls Terry's father's murder.
Joker's Moral Event Horizon with what he did to Tim Drake. That scene alone speaks for itself and this actually pushes Batman to try and KILL the Joker.
Also another case of an in-universe example when you retroactively revisit first-season episode "Disappearing Inque." Suddenly Bruce's actual display of very real concern when Inque kidnaps and threatens to kill Terry makes a lot more sense, considering what happened to his last protege when that happened...and explains why he was willing to risk himself in a fight instead of coaching Terry through an escape somehow.
The ending of "April Moon", where the unsuspecting gang leader is about to get killed. With a drill that is slowly closing in towards the camera. If you ever had a fear of the dentist, that's bound to set it off.
In "Spellbound", the massive insect world hallucination.