Prototype

You only need to focus on the story missions for this trophy. See the various boss fight trophies for tips if you get stuck on any of them, and check out the strategy in Unnatural Selection for racking up EP if you're feeling too underpowered. The Whipfist, Blade Air Slice, and Air Critical Pain Devastator will be your friends in this run as well. To buy the Air Critical Pain Devastator, you will first have to buy the Palm Slam, Critical Pain Devastator, and Cannonball upgrades.
 
This guide by uberschveinen of GameFAQs is written specifically for Hard Mode, and can help you out immensely if you are having trouble. It's written with the 360 version's controls though, so keep that in mind: https://gamefaqs.gamespot.com/xbox360/942351-prototype/faqs/56909
 
An infinite health glitch has been discovered by DarkAmon and ShadowCthulu that should make hard mode much easier for you. Start up the Disembowelment event, let the soldiers shoot you until your Adrenaline Rush activates, and then restart the event from the pause menu.

You'll lose the infinite health if you fail a mission and have to restart from a checkpoint, and during any part of the story where your powers become limited.
 
There is also a glitch that will let you start Hard difficulty with Abilities unlocked from a lower difficulty's save data. Thanks to devonm0 for detailing the glitch. I have confirmed it works on PS3, and thanks to m4jX for confirming it works on PS4. You must have completed story mode and unlocked any New Game + option for this to work. From the game's main menu, select NEW, which will take you to the list of difficulties. Select either EASY+ or NORMAL+ depending on what you have available. You will be taken to a Load screen. Select the STORY MODE COMPLETE + file you want to import and Load it. Once the Load is completed, you will be taken to a Save screen. Press  to cancel saving, and you will be taken back to the list of difficulties. Now select HARD and Save your game to start it. 
 
The game's first mission is a tutorial that always gives you a fixed set of powers as well as prevents you from accessing the Upgrades menu, but you can still check if it worked by pausing the game and selecting the Save option. On the Save menu, find your newly created Hard mode save and check that it has a + after the mission name. If the + is there, the glitch worked. If it's not, it didn't work, quit and try the entire process over again. A video showcasing how to do the glitch as well as more ways you can check that it worked is below: