Complete the game to unlock the New Game+ option, which includes data from the Demon Compendium, demon analyses, play log, fusion data, and DDS data from your previous play through. You will retain App types "Skill Expansion" and "Demon Skill+". You will also have the option to carry over your level, stats, App Points, Macca, items, and equipment by selecting the "Reincarnation Restart" option.
Start a New Game+ mode game to notice that one of four possible lights will mark your saved game file, each unlocked by completing the following tasks. Note: The "Alignment" stat is hidden, and becomes greater the closer you are to Law and decreases the closer you are to Chaos:
HOW TO OUNLOCK
Light #1 (green), Nothing Ending
Choose to become the True Messiah.
Light #2 (blue), Law Ending
Have an Alignment of +9 to +100 and complete the game.
Light #3 (white), Neutral Ending
Have an Alignment of -8 to +8 and complete the game.
Light #4 (red), Chaos Ending
Have an Alignment of -100 to -9 and complete the game.
Notice that enemies of the Horde Race are somewhat weak to attacks that hit all enemies. Since Hordes are detected as being five enemies for the game's targeting system, despite sharing one unified set of statistics like HP and MP, you can use attacks that hit all enemies (such as Critical Wave, Mazio, Maragi, and Mabufu) to hit these Hordes multiple times. This technique can far exceed the power of your basic Attacks and numerous other Skills on many occasions by at least triple their norm, and is even more useful if you use a Skill element that the enemy is weak to.
Usually when you play a New Game+, all of your party's demons are erased and you must start anew. However, if you have a demon being used for StreetPass at the time you defeat the last boss, this demon will not be deleted when you play a New Game+, allowing you to bring over super-powerful demons to your new game.