Here's the thing, the story is clearly Batman having a nightmare. None of this is actually happening and that is set out so plainly on the first page of the novel that I wonder why it's considered a big deal. The novel opens and closes with quotes from Alice's Adventures in Wonderland (because that's not overdone), a novel about an extended dream narrative (and raping children, but let's not get into that here) and the narrative and art have a nonsense, dream-like quality to them. The reader is immediately made aware that events happen on April 1, Joker even has the line "April Fool!" early on. Arkham Asylum is perhaps most memorable for the artwork, which is all painted by Dave McKean and looks great, but makes the dialogue hard to follow, especially as traditional comic word balloons aren't always used.
I don't get the appeal, sorry. The art is great, but not McKean's best work. The twist of the dream is too obvious to be clever. I like Maxie Zeus as a Batman villain, but why does he have lightning powers all of a sudden? Why are the psychiatrists so corrupt and unethical? Hell, why does Arkham need to be displayed as a corrupt and decaying institution, are all the homicidal maniacs not threatening enough? When did Mad Hatter become a pedophile? Is that just a reference to the horrible things Lewis Caroll did? Why does Batman have nightmares about being fondled by the Joker? God, this is actually really not very good at all now that I think about it. If you absolutely have to read all the classic Batman graphic novels, then give it a go, otherwise just Google Dave McKean and check out an amazingly talented artist.