To 100% the game you will need the following done:
- Complete the story on either Normal or Hard AND New Game +
- Complete all side-missions on BOTH save files
- Complete all 400 Riddler Challenges once (data is shared on both save files)
- Obtain all Gadgets and Upgrades once (data is shared on both save files)
- Obtain Gold on all Riddler's Revenge challenges (as Batman)
In other words: You will have two save files. One on either Normal or Hard difficulty and one for New Game Plus. You will need to complete the story twice, complete all side-missions twice, complete all 400 Riddler Challenges once, collect all Gadgets once, purchase all Upgrades once and complete all Riddler's Revenge challenges once.
For Riddler Challenge help, see the "Genius" achievement. For help on the Gadgets and Upgrades, see the "Fully Loaded" achievement. For Riddler's Revenge, you need all 72 Ranked medals and all 108 Campaign medals (as Batman), see "Gold Revenge" and "Campaign Gold" for help on those.