Super hero difficulty isn't too horribly hard, but there are a few parts that can be kind of frustrating. The damage it takes to take down enemies seems to be the same, but they do quite a bit more damage to you, so be aware of that. I will be outlining some general tips and then tips for specific parts that gave me trouble
First and most importantly, take your time. If you have the option to sneak around rather than just go in head first, do it.
Use the enviroment pieces to take down multiple people or stronger enemies when there are smaller crowds. It can ruin your day to have one guy that can block and screw up your combo in a crowd. Make the stronger enemies your first targets.
Plan your upgrades. For me, getting the double thread was a must so you can take down two enemies at once with the stealth takedown. Increasing your combo boost was important too so you can build up those signature moves faster. However, getting about mid game, you will need to start focusing on defense, so keep that in mind.
I would say if you find yourself having trouble, go ahead and do the side missions, but if this is your second playthrough I would skip the long side missions (such as the black cat bank heist) as there isn't a whole lot to be gained here that can't be gained from xp farming the S-01 fight. The one group of side missions I would say are a must would be the secret labs as they give you more tech upgrades.
Also, keep in mind who you do and do not have to fight. If it is possible to just float through an area without confrontation, do it. You should have more than enough xp gain from fights you either have to do or are comfortable doing, so getting into it with every bad guy you run across can get frustrating if they manage to get the upper hand on you.
Some stuff for specific parts of the game that may help you out.
During the protect Whitney segment near the start of the game, I had a lot of trouble trying to kill off everyone and keep her alive. If you have the same issue, stay right where the game sets you after they start shooting at her and just take turns webbing each of them up. It does help if your webs are stronger, but isn't absolutly needed for this. If you don't attack at all it seems like it takes a little longer, but only three guys will be shooting at her and you should have no problem keeping them at bay.
Most of the boss fights are fairly simple if you learn the enemies routine. Just pay attention to if you need to dodge, multi-dodge, or roll away. For me, the only big problems were the S-02 and Smythe.
For the S-02, the fight is pretty simple until you get to the rooftop. After you hit him a time or two his laser attacks across the rooftop can be a pain to jump over, so use your webswing. You will easily be able to clear them.
Fighting Smythe I had the same problem, but webswinging here didn't help me. What I ended up doing was hitting him with webs a few times, then web rush decently far away from him, rinse, repeat.
Other than that there really aren't too many difficult parts to work around. Just keep all your abilities in mind and take it slow. You should have no problems. If your having an issue, post a comment and I will help the best I can.