To unlock the Deep and Hard trophy in Call of Duty: Modern Warfare Remastered, you must complete the single-player campaign on either Hardened or Veteran difficulty.
Playing on Veteran difficulty isn't too hard, but there is a glitch that you can use to complete each mission on Veteran difficulty whilst playing the vast majority of the time on recruit.
The way the glitch works, is you play the mission on recruit difficulty until you get to the final checkpoint of the level. Return to the main start screen, go to Mission Select, choose the mission you have just been playing and select Veteran difficulty. As soon as the mission begins to load, quit to your console dashboard and close the game completely. Restart the game, and go choose Resume Game, and your progress will be saved at the last checkpoint, but you will now be on Veteran difficulty.
You can see a video of the glitch working below (credit to It's Ya Boy on YouTube).
You can find a list of the last checkpoint for each level below: