This is a great game, one of my favourite open world games. It has great graphics, gameplay, voice acting, detailed enviroments and good story - if you're not totally hating all superheroes, you will love this game.
The story is simple at start. Bruce Wayne (Batman's usual form) makes a press conference to shut down Arkham City - super prison build in the Old Gotham that's lead by pschyatrist Hugo Strange - but then, things get messy and he gets thrown in there himself! Then he dresses up as Batman and FUN begins! The story is interesting, it has plot twists and turns, but I felt that it's a bit short. You can easily complete it in 10 hours. Don't worry, it wont be confusing if you haven't played Arkham Asylum, but will still be more great if you have. There are MANY villains in this game. I am not going to spoil it for you by telling you their names, but there are, like, 10 of them.
The graphics are great, everything is very detailed, animations are good (except for Batman walking), the faces look good too and draw distance is very good, the snow that falls from the sky is beatiful and Batman gets numerous bruises on his Batsuit in the time of the game. It also helps that there aren't almost any graphical glitches.
The voice acting is very good throughout the game, especially Batman's and Joker's voice acting that is great. However, they hired no more than 3 or 4 voice actors for inmates, which you can notice easy. Still, the soundtrack is excellent and really helps to immerse you in the gameworld.
The main and the best part of the game is gameplay. It's just soo fun! Stylish combo-based combat system is fun and easy to learn, you can use gadgets too in combat. Gliding off rooftops is amazing, especially because Batman has ''glide bomb'' ability, with which he can cover large distances without even touching the surface. My favourite part of gameplay was the predator gameplay, in which Batman takes out baddies stealthily by moving around crouched, and, if spotted, grapple to a gargoyle and move from one to another quickly for baddies to lose sight of him. If you want to be creative, you can also use gadgets while using stealth, for example, trap unconsicous baddies body with explosive gel and then detonate it while other enemy moves towards the unconsicous baddies body to investigate. The boss fights aren't that good, they are too easy and the last boss battle has you just running around and mashing the quickfire gadget button. This game also has cool RPG-like upgrading system to get new combat abilities (my favourites are ''Critical Strikes''), upgrade your armor and get new gadgets. BTW, I recommend you to buy the "GOTY" (complete) edition, because it features Catwoman as playable character (and that is very cool, she has her own combat animations and can get to places where Batman can't), and also two more playable characters for the challenge mode - Robin and Nightwing.
So I give this game a score of 9.5! This is a great game and I really recommend you to play it. The next game in this franchise is coming out in October 25 this year, it's called "Batman: Arkham Origins" and I'm really looking forward to it, because it will allow you to explore the whole Gotham in Christman Eve!
P.S. There's a funny bug that allows you to explore the Gotham even in this game, here's a link to how to do it - https://www.youtube.com/watch?v=UvP4eQxNjQ4