One of the best games of its generation.
I played it to completion on the PS3 which is very similar to the PC version which obviously looks even better.
A semi open world, all things considered, taking place on the aforementioned Asylum. A very large collection of buildings with some action taking part outside (garden etc).
You are Batman (duh) and you, no spoilers, have to deal with certain objectives and "bosses".
You have an unlockable array of gadgets at your disposal.
There are "side quests" and secrets to be completed by you if you desire, to unlock gadgets, costumes etc. So if you are one who wants to unlock everything, there is plenty of meaty game in here to do so.
If you don't want such a thing, you can just ignore that and deal with the main quests.
When I played it till the end it was a very fun ride. Usually not my type of game, but boy was I hooked with this. I am not even a huge batman fan*.
I played it on default difficulty (don't remember if there was setting for that), and god double digit hours out of it. Unfortunately I don't remember how many. BUT, at no point did I feel like I wasn't getting enough game for my (full price on release) money, even though I did NOT deal with the vast majority of the sidequests/unlockables.
The combat is very rock paper scissors (or in a way similar to the first Witcher game) where for the vast majority of the enemies you can deal with them with any type of attack, but for the "lieutenants", mini bosses you have to use either a (very short) combo, or specific attack. I HATE combo attacks in games, but I still had NO ISSUE in this one.
When you are not fighting, and some times during, you can use gadgets and the "detective mode" where you see everything in a different color scheme and with objectives and items, highlighted, to help you investigate further your quests.
A very good game for the fans (and not only) of Batman and/or Action Adventure games.