Alright, instead of posting a 'how to' guide, I'll toss out some general tips and tricks I found useful on the journey through hard.
You can die very quickly if you're in a battle with multiple enemies, even if you're excellent with the counter button. A couple hits is still enough to take you down. Therefore, I highly recommend armour upgrades first. Second, you probably want to grab the multiple batarang upgrades, then the proximity upgrade for the plastic explosive (you get the weapon as you progress).
There are a few moves you need to master. The counter button (Y) in a fight is essential and it will take time to get it down right. Another is the RT+Y attack when a guy is down - it finishes him off. The second you have a group dazed on the ground, try and finish a couple guys ASAP. The third is double tap A (the dodge) - this will be your saving grace against large groups of goons, armed goons, titans and Poison Ivy.
In Gargoyle rooms with armed guards, there are two strategies that help. When facing 5-7 guys, make use of the Inverted Takedown. It's quiet and won't startle anyone. Also, make use of your plastic explosives and multiple batarangs, they are your saving grace - a well timed explosion or great 3 batarang shot will down a group, allowing you to swoop in and KO all 3 before they can get up. The armed goons take you down almost instantly, so you have to be incredibly careful.
As far as boss battles go...
Bane isn't too difficult if you can time your dodges and you can tap LT (the quick release batarang) - you'll catch him every time and send him crashing into the wall. The guards that help him are damned annoying, try and avoid them by running away until one or two are isolated and you can take them safely.
Scarecrow (x3) is basically a platform mini game and you'll figure out quick that going into the light is your end. Difficulty is irrelevant on this one as it's as simple as getting caught or not.
Poison Ivy gave me fits. The first half of the battle is relatively easy, make sure you use the dodge button a ton, avoiding the vines in the ground and the plant ions she fires at you. Once you blow the protective shell once, you get a save (thank god) and it's the same thing over again, just with tons of goons. I planted explosives at points and made sure to target goons near the edge as to knock them off. Basically it's an exercise in multitasking to focus on the vines as well. When she begins to shoot at you, simply keeping tapping A and LT to keep diving but also quick shooting the batarang - Batman is incredibly accurate. It IS hard but doable.
Joker is incredibly easy compared to Ivy. He's basically like a titan who doesn't charge and the battle is essentially you being able to beat up guards. Make sure to kick any close to the electric fences into them for insta kill, as well as target any guards who go for the guns. This really tests your combo skills which by now, should be good. Use the bombs Joker lets loose to your advantage - lure a group of enemies near one, trigger it and it'll stun all of them.
All in all, I found it on the same par difficulty as Ghostbusters - very challenging at points, mostly doable for the rest of the way and overall, an awesome playthrough. If you're familiar/a fan of the Assassin's Creed combat system, you may find this one to your liking/have an easier time getting good at it.