I know that this game is up there in the best of all time for a lot of people. I understand fully, but I have a small amount of problems with it. To get it out of the way, it was such an improvement from the first one. Just the gameplay alone was upgraded in a way nobody thought possible. It flows even better, and the flaws it had were patched and improved. Most of all, the boss fights felt different, like they were meant to be there. There were actually incredible boss fights, that will be remembered for a long time.
The asylum was great, but they manage to come up with a better world, Arkham City. Just with the introduction, you feel the power of this place, and the danger it brings. The main tower is impressive, and it makes traversal more complex. The gliding was heavily featured, and it became a gold standard for this franchise. In all the map, you can see a million secondary objectives you can follow if you feel like taking a break from the main story.
The narrative this time around is better, with such a good introduction to one of the main villains, Hugo Strange. He was not really known like other villains, but this game truly made him a star. My problem with the narrative is how diffuse it is. In the middle of the plot, you begin wondering what was the main objective in the first place. This happens mainly because of the Joker. Even if he is a great villain, he feels out of place in this story. All of this dissonance explodes in the final act, where the Strange storyline and the Joker storyline try to one up the other, which leads to a confusing ending that manages to end the Joker storyline, but leaving the supposed main story without the power it should have.
In conclusion, the game is a total improvement compared to Asylum, but a confusing mash of two storylines makes the ending lose the power it should have.