This, by far, overpasses Arkham Asylum, but is more innapropriate for these reasons:
Violence- 4/5 While this follows the same combat system, it is more violent. The hand to hand combat is okay, but on the last knockout blow, it shows it in a slow, dramatic fashion. There are scenes where armed thugs take hostages, and if they see you, they shoot you. There is a scene where a cop, wearing a shirt that says "Dead Cop", is shot by penguin. Towards the end of the game **Spoiler** Ra's Al Ghul stabs Hugo Strange, and his shirt is stained with blood. In the game, Protocol 10 is shown in action, which is basically a bombing of Arkham and Gotham.
Sex- 3/5 Throughout the game, thugs say sexual references, such as "I could go for some p--n right now, or "Easing sexual tension." Catwoman's shirt is zipped down far her front, showing a large amount of cleavage. Also, her skimpy outfit shows the outline of her buttocks. Harley Quinn wears a shirt that shows a lot of cleavage, and she wears tight pants. In the Harley Quinn's Revenge (GOTY only) Robin reaches into her cleavage and grabs a card. Poison Ivy wears a shirt that is partially unbuttoned, showing cleavage. She also walks around in tight-fitting panties, showing part of her bare buttocks, and her butt crack. On a building, there is a sign that says Live Nudes with a silhouette of a nude woman.
Language- 4/5 First of all, "Mild Language" does NOT suit this game, for it should be just "Language". Throughout the game, a--, p---, b------, h---, d---, and b---- are heard, with the rare "Oh sh--, it's Batman!" (not in subtitles). In Catwoman's story episode three (GOTY only) one of the TYGER guards yells f---.
Drugs/Alcohol- 2/5 This isn't a problem, just some drug references and alcohol drunk.
Ease of Play-3/5 This game has a kind of combat system used with a stun button, strike button, run and jump/glide button, and a counter button. During combos, you can use quickfire gadgets, and the gadget will count in the combo. For example, if you are surrounded by thugs, you can use quickfire explosive gel (LT+ X) and it will temporarily incapacitate them.
Overall, this is an amazing game, but parents, don't think "Oh, it's Batman, my 9 year old will like this." Arkham Asylum took a dark turn in the Batman franchise, but Arkham City went darker. For mature teens and up. I hope this helped : )