As a Batman fan I have to say that I really enjoyed this game! :)
Yes, it's a handheld port and all, but even then it's a pretty decent game.
I read mixed reviews which said that the game sucks because of poor graphics and bad gameplay. I wont comment on graphics, because I don't play games for graphics, and nobody should. About gameplay, well here were a bit of problems with controls and there were some stupid game mechanics that became very annoying after a while!

About the controlls first:
The controlls are pretty responsive, but there were some times when you had to do/press a button multiple times for it to work, which can get very annoying after a time, especially if you have to hury because a timer.
For example: When you do the bomb hunting/hostage rescuing at the end of the game and you have to enter a went by holding the A button on a 360 pad, and it wont register after a few times, not until you go away from the went hole and go back for it to show the (Hold A to Enter). This is very annoying!
Other problems I didn't encounter with the controlls, other than this, the controlls are great and very easy to learn.

Mechanics:
The only annoying mechanics in the game for me was the Scanner!
In the beginning I thought of it as a neat feature, but after a while it got so annoying that you had to do it almost every time for you to go on ahead! Even for things that were staright forward and didn't need any further explanation!
Other than this little annoying thing, haven't really got any more issues with the game.

The game itself is on the shorter side because you can beat it in 3 or 4 hours most IF you don't do any side content and exploring! Your very first playthrough may be a bit longer if you like to stop from the main story and do a bit of exploring.
Keep in mind that by exploring I don't mean to explore the entire map or anything like in the past games, because this isn't a full 3D game, it's just a 2.5D platformer, but believe me that you can get lost very easily.
I myself, when I did my first playthrough of this, it took me roughly 15hours, because I did collect everything and did all the side content, but my other playthrougs were only about 3 or 4 hours as I said earlier because I just rushed from start to finish to get all the endings.

And yes, it's true that you'll have to do a bit of backtracking when you hunt for the collectibles, but it's not that bad!

From my experience and for being a huge Batman fan, with all the little flaws that this game has, I'll give it a 7.5/10.
It's not a great game, but it's not bad either! If you like the Batman series or Batman in general, I think that you'll love this too!