I bought this when I noticed it was 69p and for the price i'm rather happy with it. Anyone who paid £4.99 will most likely have more negatives I'm guessing.
Anyway, its open world with missions set within Gotham which so far have been following the films story but not exactly the same in structure or settings but thats a given to be fair.
It controls well enough, but moving the camera can be annoying on touch screen, you'll sometimes press jump while trying to spin the camera round. The combat is very simple but fun - it has a dodge, attack and when you need to block it quickly flashes on screen for you to press, if enemies have a weapon you can use the grapple to disarm them which is a nice touch.
Visually it's pretty impressive, not as good as reviews have said, but its still a tidy looking game. One thing I have to mention is the voice acting, it's hilariously bad. If you found Christian Bale bad with his asthmatic Batman then the guy performing this voicework will really annoy you. I keep thinking of those YouTube videos that were taking the p**s out of Bale, its just so bad it has to be heard or seen if you get the chance.