In the area where the final bounty hunting quest's target is there's a ladder going down, where you'll find some of the elf village survivors. This will enable a quest that requires you to find them a place to live in the slums.
Going to the rogue adventurer's house in the slums you will find someone that has taken it for himself, and will sell it for the astronomical sum of... 1000G :P
Pay him and the elves will come and occupy the house.
Go to the atelier and rest to find how much they were able to fix it up.
After that, they'll ask you to get them 10 fine roasted beef.
Completing this final quest will have them tell you that using the amulet that the elf elder gave you before she died allows you to modify space-time circles.
Having this knowledge and going through the normal ending of the game, you'll be given the chance to modify the destination of the circle that takes you back to the present time after beating the golden dragon.
Doing so will teleport you back to the elf village at the moment it was attacked, allowing you to fight Hart, Tessa and the goblin army.
Hart will summon a few more goblins after cutting down his HP.
Tessa on the other hand will request the usage of a Divine Lightning spell, which packs A TON of damage (I recommend using the final defense spell that makes you impregnable to damage for a short while)
After defeating them all, you'll be able to get to the elder's house, where you'll see the Hero ending the Goblin King, queueing the ending credits.

After reaching the 5 star atelier status, go to the Altona castle.
There, you'll find red knights using a password to enter a secret base. Follow them and you'll meet the Golden Twilight's boss' true identity, and the final member's as well: the queen.
End the transformed red knights and the queen to enable you to go back to the castle and the usage of a time-travelling circle that sends you to the past.
There, you'll find many more of the transformed monsters. Finish the 2 waves of this monsters to face the 1st phase of the final boss: the Messothian (the ancient civilization) Viceroy, where you'll be joined by Millia and your boss, who'll help turning off the barrier that was protecting the boss and its minions.
After beating it, you'l be warped alongside it to the same chamber where you fight the ancient dragon, where it'll be transformed into a golden dragon.
After beating it, you'l be regarded as a hero by the sea-dwellers and sent back alongside Millia to the present time (your boss stays, as she finds it to be a fun place/time to stay at).
After being regarded as a hero in the present as well, you'll see Atelier Sheryl being overrun by clients, and Sheryl and Millia tending to it. Also, we'll be shown a scene with the elf village's spirits thanking you for avenging them as they disappear. Also, here we'll learn that the elf elder was our boss all along. After this scene the ending credits begin.

Conditions: don't be a virgin and go back to the present time after defeating the final boss.

In this ending, Sheryl and Millia decide to travel around the world, leaving Debora behind handling the atelier.

Conditions: defeat the final boss and going back to the present time; lewdness at max value; possibly employing a few escorts & working at the brothel

In this ending, Debora handles the atelier, while Sheryl and Millia handle the brothel.