It's a very good thing I finished Batman: Arkham Asylum the first time in "normal" mode. If I had started the game on "hard" mode from the very beginning, I would've stopped playing in frustration. The meat of this game lies primarily in all the brawls you encounter throughout the game, and the "hard" part of the game is mostly from the enemies being stronger and more aggressive.
There are little aspects, too, that are ramped up in difficulty. Unlike the "easy" and "normal" modes, "hard" mode has no more of the Bat-sense halos over your enemies' heads during fights, so you'll truly need to anticipate their attacks to properly counter them. Also, they've decided that only in "hard" mode will the enemies be able to crane their necks and look above you, possibly catching you perched high up there in your seemingly-undetectable gargoyle and shoot you down.
In the end, I persevered through the tough battles, often spending up to a half-hour trying to pass the more endurance-driven bouts without being killed. Would I do it again? Hell no. If I'm gonna enjoy the story again, I'll play through it in "easy" mode next, just to equal things out. In the meantime, I'm looking forward to some more free content coming later this week!