As the description says, you need to Defeat the Queen of Ice at Ice Castle, which is the last level in the game.
The key thing is to say "Never!" when Toya asks you if you are ready to kill him. If you say yes you will get only the Decision achievement and the game will end. Say no, and you still have to fight Toya, but by not killing him you get to fight the Queen.
As for killing the Queen herself. First, make sure you use the healing station just before the stairs up to her. She starts out with 8000 HP and obviously is a Water Ether character. Her main attack does around 550 PP, double against Fire based characters. After you kill her the "first" time, she turns into her "true" form and you go again. This time she has 12000 HP and can do 600 - 800 PP of damage.
Try to come in with maxed EX and use your strongest Fire based attacks. Make sure you come with max (9) potions. There is a shop right there at the stairs for this. Since your TB isn't useful after this use any remaining to pick up some Skill Gems and add some more SP to your party.
I didn't find her all that tough, but I did go in with some pretty maxed lvl 60+ characters. Also bring at least one, if not two characters who have strong healing spells - but not one that is Fire Ether based - try for Water based. Someone like Karin who can heal and doesn't take as much damage.
Atsuma is your biggest damage dealer, but he'll also get pounded. Use someone like Ralgar to clear out her support so Atsuma can get a clear shot at the queen. Use the other characters to keep Atsuma alive.