The first thing that I'd change would be un-killing Arkham in the show.
I honestly think Arkham was nerfed in the show. His in game counterpart sought out Lady's mother (Kalina Ann) specifically for her heritage being associated with Sparda and sacrifices, and only had a kid with her with the intent of sacrificing them both (as far as I can remember) He was evil from the start and had been planning the everything leading up to dmc3 before he even met Kalina. Compared to in the show, seeing a demon for the first time and having a psychotic break and searching for power after that.
Arkham would be the secret antagonist working behind the scenes to put everything in place for his plans. I don't mind the White Rabbit taking center stage for most of the show, but I want to keep in line with a little bit of the mangas story. (I won't rewrite the whole story here, but I'll write out the Arkham centered parts)
(I refuse to spell out White Rabbit ever time I mention him, so I'll refer to him as Rabbit)
I don't want to repeat the exact story in the game, so the idea of using the sword to open the rift to the demon realm can stay, but it's going to happen in a temple because it'll look cooler.
In the context of the show, Arkham would probably find Rabbit after the warehouse bloodbath. Taking him in, Arkham would want to test demon blood infusions on someone else before himself, or Rabbit could come up with the idea on his own once he recovered. Arkham would manipulate Rabbit into hating darkcom and specifically Lady to steer his anger. Rabbit is one for theatrics, so he'd probably play the role of a more genteel jester if going by game plot beats.
Vergil and Rabbit would have a small rivalry,(yes Vergil is here)made worse by Arkham sending Rabbit to collect Dante's half of the amulet.(He did that on purpose) Vergil definitely thinks he's above sucking up for validation, he'd just look down on Rabbit and talk up how much more capable he is. Rabbit would have almost the same disdain he has for Dante and Vergil, only slightly less for Vergil because Arkham lies to him that they are going to help the refugees, and assumes that Vergil wants to atone for his father's crimes.
To play out Rabbit's story arc, someone will reveal Arkham's true plans in front of him, depending on how emotional the scene should be or who works best for his final battle, I think Lady should kill him like in the show, it just won't involve Dante doing most of the work. Arkham would be the best to say it, probably in a "you're no Maria" (sonic 3 movie) way, telling Rabbit he meant nothing to him and he was only a pawn. Having all that infused demon blood and emotions running high would cause him to lose control after finding out he's been working for a lie. Or Arkham had a kill switch on Rabbit as a contingency plan, and sets it off to escape Lady. Arkham would turn the situation into blaming Lady and sending an out of control mutant Rabbit at her. Lady would have to confront Rabbit's anger at her being similar to her own anger at her father, which would lead into the part in the game where Lady accepted Dante going to kill Arkham.
Arkham's plotline is going to end with him taking the power of Sparda like in the game because that was great.
Having Arkham as Lady's reason to fight makes more sense than "we saw a devil and it was really scary, it scared daddy so much he shut himself in his room and went crazy, turning himself into a devil, and then he killed mommy, so now I hate devils and blame them for all the bad things that happened" isn't exactly the best motivation, especially when the devil in question never even touched the family and died before doing anything. Sure it was scary, but not really a reason to want to kill all devils.
If anyone has seen/read chainsaw man, I'm basing Lady's motivations to join darkcom off of Aki. Having her join darkcom because they have the weapons, budget and numbers to kill her dad is a stronger reason than her hatred of demons.
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