Slash Mode
To unlock slash mode you simply have to get ten of the twelve supporting characters. It does not matter which ones.
Play as Katze
To play as Katze you must beat slash mode in under 15 minutes with any character from the Shainto school.
Play as Female Gunfighter
To play as the female gunfighter (what is her name?), you must beat Slash Mode in under 15 minutes with any character from the Narucagami school.
Kabuki Characters
By beating the slash mode without dying you will aquire one kabuki character per school. This means you have to pick one fighter from each school and defeat the mode twice. The time doesn't matter and I would suggest Suminagashi from the Narucagami school and Gengoro from the Shainto school.
Hundred slashes mode
Complete the game with the six regular characters.
Chanbarra mode
Defeat all thirteen Bosses in action (Boss) mode without using any continues. Highlight the "Link Mode" option on the main menu and press Down(2) to access Chanbarra mode.
Fight as sub-characters
Complete decisive battle (story) mode and keep both sub-characters alive. The sub-characters may now be used in any other game mode.