Organization XIII Data Replicas are optional bosses found in Kingdom Hearts II: Final Mix+, found in the Cavern of Remembrance. Once Sora, Donald Duck, and Goofy reached the Garden of Assemblage, they could access a computer that would reveal doors that correspond to each Organization XIII member that they defeated. If Sora accepted the challenge from a door, it would warp Sora and his friends to wherever they fought that Organization member, and a data replica of that member would appear and fight them. (for example, if Sora accepted the challenge from the door with a sitar on it, they would be warped to Radiant Garden and a data replica of Demyx would appear and fight them.)
These battles are extremely hard, with each data replica having about the same amount of HP as the Marluxia Absent Silhouette.
The Axel and Xemnas battles are only available after beating the game. The Xemnas challenge consists of two battles: the one at Memory's Skyscraper, and the final battle in which Riku helps you.
Also, the order of the doors is the same order in which the members sit in their thrones.
Xemnas: As I said earlier, this consists of two battles: one at Memory's Skysraper, and the final battle in which Riku helps you. Xigbar: Battle at The World That Never Was. Xaldin: Battle at Beast's Castle. The Beast does not help you. Vexen: Battle at the Old Mansion. Lexaeus: Battle at Castle Oblivion. Zexion: Battle at Destiny Islands. Saix: Battle at The World That Never Was. Axel: Battle at the Old Mansion. You are alone for this battle. Demyx: Battle at Radiant Garden. Luxord: Battle at The World That Never Was. Marluxia: Battle at Castle Oblivion. Larxene: Battle at Castle Oblivion. Roxas: Battle at the Station of Serenity.