To access Star Ocean 4's first post game dungeon, you must go through the game as normal and beat it. Save your clear game data when prompted, and load it. The two doors in the final save room should be open. The foor to the lef leads to a dragon boss. Challenge it and defeat it to recieve the darkness ring.

Leave the dungeon and go to the Tatroi Colisseum on Roak. Head beyond the reception desk and go to the far back of the left hallway. There should be a light barrier blocking a doorway here. Remove it with the darkness ring and enter.

In this room is a glyph that will transport you to the Cave of the Seven Stars.

Welcome to the first post game dungeon! Now watch and enjoy as your party is evicerated by its powerful enemies and bosses.