When you beat the game once and make a 'Clear' save of it an 'Extras' menu will become an available option at the 'Main' title screen. This menu offers a database with information on Monsters, Recipes and Alchemy items and any ending portraits based on your saved games which you now get will be added to a gallery. You can also view ALL the unlocked endings and listen to messages from the Japanese voice cast.
When you have beaten the game once and 'Saved' the file, reload any 'Save' before the last boss and go to the World Map. At the world Map go to the area called 'Old School Building' and to the section called 'The Forbidden Zone'. There you will find a teleporter in the dungeon which will take you to the bonus dungeon which has monsters including the final boss monster which are more powerful with different abilities. There is also a boss cameo appearance from Atelier Iris 3.