NOTE #1: The Sephiroth battle is not available until AFTER revisiting the Space Paranoids level (when you fight the MCP). Once that's done, you can find Sephiroth at the Dark Depths. Walk up to him and use the APPROACH command to trigger this SUPER difficult and frustrating battle.
NOTE #2: To trigger the Rematch Of Fate cutscene, defeat Sephiroth first. After the battle, go back to Radiant Garden Square and talk to Cloud. After that, go BACK to the Dark Depths and talk to Sephiroth to trigger the cutscene. After the cutscene. Tifa hands over the Fenrir Keyblade.