This needs no introduction, heck it shouldn't even need a video:
[video=youtube;EmcMG4uxiHk]http://www.youtube.com/watch?v=EmcMG4uxiHk[/video] ^^ As always, this is an external link, play with caution.. and I can't ever seem to find good videos without foul language..
Dark Souls is known for being a particularly difficult game to beat. I have only played the game once (yes.. I got that uninterested that quickly) but it was challenging. The enemies are difficult and you lose your materials whenever you die which requires you to survive without dying in order to be successful. This sounds silly at first, but once you get into the game you'll feel the challenge. I keep telling myself I'll go back and beat it someday, but new games keep being released and I never have time.
As far as 360 games go, I'd say Vampire Rain. I haven't bothered to try playing it in years, but maybe... 5-6 years ago when I first tried it seemed impossible You rely heavily on stealth which I wasn't really fond of, and as soon as you were spotted the enemies seemed impossible to kill. Maybe if I tried playing it now I'd have better luck... but who knows
I'm not a huge gamer but I honestly haven't played too many that *were* all that challenging for 360. Some have irritating controls, or glitches that leave a lot to be desired, but I haven't played anything that was too hard to beat for me.
It would either have to be Super Meat Boy or Dark Souls. Each of the two are extremely difficult games, although they both achieved this level of difficulty in a fair manner. If you fail in either of those games, it was because of your own error, and not some unfair mechanic.