Descend to the Core
Leave the cave that contained the Ribbon chests and head to the right. Go to the right and all the way around the room until you reach the staircase. Go down the stairs and into the opening on the next level. You will finally be inside the Moon's Core. Inside the core, the enemies will be the toughest you have encountered in random battle. Make your way through the room until you reach the staircase, but don't go down it yet, head as far south as possible, and you will find the final weapon to be obtained from the Subterranean.
Ogopogo is similar to Leviathan, except Ogopogo will use the Big Wave attacks more frequently than Leviathan. There is no real strategy for destroying him, except attacking with the strongest attacks possible, and having Rosa use cure spells every round. Once you have obtained the sword, have Edge equip it.
Down the Passage
Go back to the staircase you just passed and descend further. In the next room, weave your way around, going to the right, down 2 staircases, then to the left and down a staircase, then to the right again until you get to the next set of stairs. In the next two rooms, follow the same basic strategy, weaving your way through the room, getting any chests you like along the way. Eventually you will enter a room where you will find FuSoYa and Golbez fighting Zemus.
As you enter, Golbez and FuSoYa engage Zemus in battle. It appears that they have defeated him, but he transforms and defeats both of them handily. Suddenly, your friends from earlier appear, and begin to heal you, allowing you to recover to fight Zemus yourself. Now you will begin the final boss.
The first thing you must do is have Cecil use the Crystal (available from the Item menu) on Zemus. At this point he will transform once more into Zeromus, and you will be ready to attack. Zeromus has several different attacks, including the Big Bang which will attack all of your party at once, as well as the Blk Hole which will remove all status conditions from your party. He will also use some strong Black magic spells on you. The key to this battle is to have Rosa constantly use Cure4 on your entire party. This will ensure that at least most of your party will survive each round. Use an elixir on her when she needs more magic. If you have enough experience, you should be able to defeat Zeromus using this strategy.
At this point you will see all the people from the game once again as they come to Cecil and Rosa's Wedding. You finished the game. Congratulations!