I couldn't help smiling at your question. Arkham Asylum is a Batman book, ... and my husband loves it! The full title is actually Batman: Arkham Asylum. This particular book is the very one that is known to have launched the careers of both Morrison and McKean. Further, it's still considered one of the very best of the Batman stories.
Unsurprisingly, this book is about Batman's dealings with the inmates of Arkham Asylum of the criminally insane (which now houses lots of his previous nemeses: Two-Face, the Scarecrow, the Joker, Poison Ivy, the Mad Hatter, etc. Not surprisingly, this asylum is located in Gotham. These notorious inmates stage a mutiny on April 1 (April Fool's Day) and take on hostages. They demand the character of Batman in exchange for those hostages. The notorious inmates hope to corner Batman out of where he is comfortable (on Gotham's streets) and where he doesn't have access to his cool, high-tech crime-fighting gear.
Batman accepts the challenge of his formal rivals at the asylum. As a result, he is faced with what each considers the ultimate torture. Batman's goal, of course, is to save the poor hostages and return this asylum (which, of course, is really a prison) to its former glory. We could go through each personal hell for Batman, but that is the fun of the book. Just know that there is one for each rival: one for Two-Face, one for the Scarecrow, one for the Joker, one for Poison Ivy, one for the Mad Hatter, etc. Not surprisingly, Batman faces each challenge with pride and bravery. Further, Batman "wins" each challenge and is able to incarcerate each former foe, save the hostages, and return the Arkham Asylum to its original house for the criminally insane.
In addition to the Batman plot, there is also a side plot about Amadeus Arkham who began the asylum. He is a dark character as well who has as much a problem with his own mental issues as both his inmates and Batman himself (as he is faced with the challenges).
In conclusion, please know that as Batman faces each of these strange challenges, he is forced to face all of his previous foes AS WELL AS some of his inner demons. The fact that Batman wins out, yet again, is a testament to his character as a person as well as his character as a super hero.