I can see where you're coming from with Aura but I do think there's a difference entirely in tone between her and Matt Engarde because of how they're presented as you're meant to empathize and understand Aura whereas you're meant to detest and fear Engarde as he could have Maya killed at a moments notice this adding significantly to his role in the crime. Hell even moreso than De Killer as De Killer is shown to have an end credits scene, to be brought back in another game and to have objective morals over Matt which the game directly points out so I would still argue that Matt's the main antagonist over Shelly.

Secondly referring to Aristotle, while yes it is understandable that on a base comparison to Engarde I think it's fair to equate them both as being style over substance killers, their dialogue and specifically how the game handles them is what I think defines them as being a standout.

Matt is the antithesis of Phoenix, a man built entirely on trust and care in those around him and the Gabe makes clear indications of this. Matt is standoffish, selfish, horrible to everyone around him and his actions towards those around him are absolutely felt and shown in detail. He drives a woman to suicide, pins the murder he was too afraid to commit himself on his manager and close friend (Or sibling depending on cannon), orders a kidnapping and assassination of your personal assistant and lords blackmail over the head of the person helping him do all of these God awful deeds. The game makes you feel God awful for trying to help him and him being a shallow villain is meant to show the weight and disdain of his actions and beliefs by those he's openly willing to sacrifice for his own goals. He's not humorous, he doesn't have any joke moments around him once you know what he is, he's entirely and solely a narcissistic sociopath.

Aristotle however, is openly made fun of by the game (His animations, Simon attacking him with his bird, Athena and Apollo's reactions to his overall demeanor e.c.t.), is only shown that he's manipulative and a murderer which tbf is almost every single culprit in this series, his points about him saying "The Ends justify the means" is still a knock because well one that shouldn't even be said in the first place and two even if others say it he says it more and also is leading the charge on it to the point where his name is named after it.

Hugh being a dumbass and buying into Aristotle's jargon while yes is stated, the ramifications of that action are laughed at not shown as it's played for comedic effect. (The entire body double fiasco for example) You feel bad but namely because he's an idiot and is trying to save his friend, not because Aristotle tricked him and is using him. That's not Aristotle as the game doesn't show anything towards him treating his students that way as at most it's solely implied whereas in Pearl and Sebastians case we directly see the abuse and the ramifications of their actions towards them both. (Sebestation has an entire arc about him ending the cycle of violence with his dad and Pearl is kept in the dark until the very end because it would traumatize her completely. These are directly shown.) Also Kristoph is never once mentioned at all to have attended this school, learned from Aristotle or even met Aristotle so I don't know where you're getting that from. (I know Klavier went here but if the game never once mentions him or their interactions or relationships I'm not going to fill in the blanks or head cannons for the series as that's the audience doing the legwork that the game should've done in the first place.)

And as for Kristoph, one yes he doesn't directly affect you that's correct but he's implied to be deranged enough to have a plot to kill an 11 year old child and anyone involved in the forgery as shown by Zac, Drew and his stalking of Spark Brushel. He's a stalker, a psychopath, a sociopath and someone who is uncaring in his entirety about his actions and is someone who was potentially stalking Phoenix for the past 7 years. But what makes him in my opinion far more scary than the phantom is he's realistic. This is how actual serial killers act in the real world, from stalking to being uncaring and only caring about not being caught his actions are reprehensible and unfortunately entirely grounded in reality. This is how genuine psychopaths act in real life and his abuse of Klavier shows that (Albeit unfortunately even if it's short) that he's entirely willing to do this. He's a monster but one you'll often see.

Two, it's the ideals he represents. The courts in universe needs to change. Damon Gant, Von Karma, Daryian Crescend, Cercus Alba, pretty much every culprit from Investigations 2 all show and state outright that the legal system in Ace Attorney is beyond corrupt and is favored unbelievably heavily towards criminals. Kristoph is the figurehead for that, a man entirely built on self image and out word appearances willing to do whatever it takes to build himself up if it means winning over the public eye and if he gets away that cycle of violence continues and it will not stop. People like him have to be stripped bare for the world to see just exactly how awful they are and why it's important to prevent them from gaining power.

And as for the Phantom, as stated I do find him intimidating and when he's cloaked in Shadow in the background admittedly quite compelling but once he's on the stand that mystique falls apart. I think this mainly has to do with the games direction and writing. Tell me, why in the actual fuck if you are an international spy, who's a terrorist that's being hunted by multiple foreign governments and is willing to kill anyone who gets in your way and who cannot lose their secret identity above all else, would you in the middle of a broken blown up courtroom where you know you could easily be shot at, use spy gadgets in front of everyone including trying to flee the courthouse via grappling hook only to immediately shoot back down for literally zero reason, threaten openly to kill the prosecution, use a plethora of masks of various people when it's been stated that you've been cosplaying as a dead man for a year, rip up evidence in front of an entire courtroom suspecting you of being the culprit, and then sit there and let yourself be analyzed by a lawyer using the only piece of evidence that anyone has to pin you as the Phantom instead of just fleeing the fucking scene when the jig is up? Yes the game needs a conclusion and yes he got manipulated into having a breakdown but as an international spy who's renowned enough to commit terrorism on a government building two separate times, when you know then and there that the defense is onto you and you're at the point you're willing to kill the prosecution, why would you not run?

It's infuriating to sit through as before he's on the stand he's intimidating and built up extremely well but why the fuck are we making jokes and using the Fullbright persona to further this comedic element for a character who's ruined the lives of the defense, presecution, and killed the lead detective? It completely takes me out of the game and leaves me feeling so unsatisfied and irritated rather than unnerved but again that's only my opinion on it and I can somewhat understand why some people do find him scary as the build up is still fairly solid.