An amazing game, far better than Arkham Asylum. The open-endedness is really fun, as is beating the shit out of thugs.
The story is engrossing and the character constructions are great. All the little explanations are useful too, since I'm not a BatMan devotee and don't know who people are. The little stories you unlock by solving riddler challenges are cute too.
A few cautions:
Firstly, this is a console game. This is not a bad thing, but is it of the genere of games that inherently are not suited to mouse usage, being neither point'n'click nor aim'n'shoot. You will want to grab a gamepad for this. You can get an official MS one for about £17 or a third party one cheaper. They work for loads more games than just this one so it's a good investment.
Secondly, the graphics are badly optimised. Disable dynamic shadows and go one peg lower than normal. They still look phenominal regardless, so bite the bullet and enjoy FPS based breathing room.

Good fun cathartic violence with pretty graphics. Not a particularly original idea (I've played at least four flash games with exactly the same synopsis, even ignoring l4d), but the gameplay works well, and as I said above the graphics are very nice. It does have a few oddities, but the developer is receptive and very responsive, and said he/she would fix everything I could come up with in the next update, so no complaints on that front.
My one gripe is that there were no public MP games when I tried, but ignoring that, this is definitely worth the money.
TL;DR: Good easy on the eyes timewaster. Buy it.

!!!!!!DO NOT BUY THIS GAME!!!!!!
While containing facinating gameplay mechanics and acceptable graphics, you are unlikely to see them as the game consists of nothing but a multiplayer mode that DOES NOT WORK.
The server browser is impossible to use and will automatically show all the full servers first, which you CANNOT CHANGE.
I have no idea how there are so many full servers, as any game I attempted to join (which helpfully spammed all my friends with "Lexi is now playing Breach. Click here to join." every time I queried a server) either hung for 10 seconds then said "FAILED TO JOIN GAME", or connected, let me watch a cinematic for 17 seconds, spawn and then quit to the menu with "CONNECTION LOST!!".
These popups have to be closed with the mouse incidentally, as the keyboard is unavailable while in the menu state, which makes browsing menus annoyingly slow.
Perhaps the reason the game was so unreluctant to change from 1024x768 was that going any higher makes the buttons too far away.