New Game +
When you beat the game, stay after the credits and you will be asked to save. Save and reload your file with a star icon and you will be able to start the game with your Blue Weapons, Blue Armor, Blue Stones, Blue Titles, Dragon Eggs, Playtime, Mystic Stone Grid, Ancient Cave (Now goes up to FL100), Tutorials, and Combat Notes. Jessy will continue your Soul Shard count (Max of 600 are carried over, but now goes up to 1270), and when Iris joins your party, she will give you any blue items you didn't unlock from Jessy from your previous play through.
Upon completing the game a second time via New Game + you will be presented with an additional boss fight, win and you will be rewarded with an alternate ending.