Woohoo! Finished the game on hard. The battle with Ivy took me a lot of tries, mainly because the camera angle isn't ideal and it's tricky to see who is where. I found it easier once I concentrated on avoiding the vines and picked off the henchmen a bit more slowly. You kinda have all the time in the world with them, and if you use the batclaw to pull them over and let them get tangled in the vines instead of you, then you can buy yourself a lot of time.
After that I nailed the battle with the two titans in one try, no idea how, and the battle with the joker only took me two tries.
Just need to get Gold on the two challenges now... I'm expecting Predator to be a hell of a lot easier than Combat.