Hard mode = Enemies do at least 2x damage (it seemed to me like some spikes did 4x damage, but I'm not 100% certain). Ability tree takes more points to fill (54 ability points to fill the entire tree on Normal, 75 points to fill the entire tree on Hard). I don't think there were any other major differences, but I did die twice as much as my WORST normal runs these days (died about 15 times on hard mode), so it does make a difference.
I'll update this if I nail down any other specific changes, but that's the main stuff. It's really not that bad. I would suggest exploring for Life and Energy cells, but don't do your 100% clear run on Hard because there aren't enough Ability Cells on the map to fill up your ability tree on all 3 branches. Focus on the top branch (triple jump) and bottom branch (stronger spirit flame and other powers).