While on Nightmare mode you need to complete the last chapter prior to the credits. Unlike the standard story mode, you will be timed, so you must focus more on completing story missions and getting the items most important for finishing the game.
You can either do Nightmare Mode first, or wait until you complete Story Mode and turn Nightmare Mode into basically a New Game +.
Note: You can also get this by joining a friends game if they are in Nightmare Mode Chapter 7 and completing it with them without doing the first 6 Chapters yourself.
It's worth noting that you don't have to do this in a single run like the Survival modes in the previous games. You can save, it's just that you can only save using the toilets. Very quick and easy to do if you just focus on doing the yellow case missions and ignore everything else. I'd actually rank it easier than normal Dead Rising 1 & 2. Pick up some good combo weapons. I like to keep a few Jazz Hands for clearing zombies, a few Boom Canons for slow bosses, a few ZARs and a bit of food.
I did this in 2-3 hours at lvl 50 with all the possible upgrades. It is very easy, use lots of vehicles to get to places faster and also have your entire inventory full of the "Spread Shot" gun, I think it's called that at least (The combo of lead pipe + assault rifle) and it's a brease.
I'm on chapter 3 (almost done with it) on nightmare mode if anyone wants to join send me a message or if anyone has a game at chapter 6 and would like to invite me please do my gamertag is PuRe Emerald thanks :)