Start off by going through the north door and then going through the north door again. Riku is outside of the mansion now, and wonders if Naminé is inside. This is when his replica shows up. The replica is angry since he just recently found out that he's a fake - just a replica of the real Riku. As long as the real Riku is alive, the Riku Replica is nothing but a shadow of the real Riku. He then proceeds to attack him, and the boss battle begins. Facing your replica isn't much different than the last time you faced him, except this time, he has a new move. He can now use Dark Aura, one of the most useful moves Riku can use when entering Dark Mode. He has three health bars as well, but other than those two changes, it shouldn't be much different. After the battle, the replica, now finally defeated, starts to fade in and out. The replica asks Riku where his heart will go when he dies, since the feelings he's experiencing at the moment probably aren't even real. Riku answers him reasonably by saying his heart will go wherever his heart goes. The replica, satisfied with Riku's unoriginal answer, fades away completely.
Use the left door. In the next four rooms, use the north door. A cutscene will follow where Riku meets Naminé. Naminé offers Riku a lock on his heart that won't let Ansem out. He asks her if he'll lose his memories in the process, and when she doesn't answer, he asks again. She says that his memories will be locked away along with the darkness. Riku rejects the offer, and tells her that the darkness will help him show the way. She says that that's the truth, and he asks her why he knew she'd say that. She says she doesn't know, and then he answers his question by saying that she was the one that appeared to him as Kairi in the light. She's shocked that he was able to find out and asks him how he did. He says he knew as soon as he met her and that she smells the same as Kairi, somehow. He smiles and walks away, telling her to look after Sora, and then leaves.
Use the south door in Room 6, the south door in Room 5, the south door in Room 4, the right door in Room 3, the right door in Room 2, the north door in Room 7, the north door in Room 8, the north door in Room 9, and the north door in Room 10. You'll end up back at Castle Oblivion.