Just like the previous game, there is no real secret or trick to this one. Start a new game on Super Hero difficulty and just play out the main missions (14 total).
Down on the directional pad is the Heal ability. You may need it from time to time.
Missions are not hard at all, and made easier if you go mostly stealth. If you are having difficulty with a crowd, back off and wait for them to lose track of you. Also, webbing an enemy up, and then doing a 3 hit combo will result in an enemy ready for a finishing move (B) 9 times out of 10.
Brutes are not hard once you get their rhythm down. Shockwave, 4 hit combo, then roll away. Rinse and Repeat.
Bosses are also fairly straight forward - all of them can be countered/dodged. Just melee afterwards and you should be fine. If you are having difficulty with a boss, leave a comment and I will offer some advice.
In terms of upgrades, I found getting the web pull ability maxed early on was very helpful. Guys with guns will seriously drain your health if you are not careful, so just ripping it out of their hands, and webbing it to the ground, will definitely be beneficial. After that I focused on web strike, and then the seismic blast.
If you are hesitant to start this on the hardest difficulty due to an unfamiliarity with the game mechanics and style, don't be. You will catch on quick to everything the game throws at you (which in retrospect is not a lot at all). To make things easier, especially if you are going to remain mostly in the shadows, start yourself off with the vigilante suit. This will also help keep the Heroic level up (as you do various side missions) so that you do not have the added annoyance of the aerial enemies coming out of nowhere and being a pain in the ass.
As you progress through the game you will unlock more costumes - I highly advise using them when they become available, especially
Questions, corrections and neg vote justifications below.