To unlock Perfect mode, complete thirty songs. Then, go to the song selection screen, and press Down/Right to display the options. The Perfect mode icon resembles a yellow Don wearing a gold crown. In Perfect mode, one missed note will result in a failed song.
To unlock High-Speed 4 mode, complete thirty songs. Then, go to the song selection screen, and press Down/Right to display the options. The High-Speed 4 mode icon resembles an animal with an open mouth with a red flag next to its name. In High-Speed 4 mode, notes will scroll 4x faster.