To get the alternate ending sequence you must successfully complete the game without using any continues.
A screen with a globe will appear before the next fight begins. Hold Select while the globe spins, and keep that button held until the screen fades to display the controller configuration screen.
To fight as a boss quickly press B, A, X, Y, Up, Left, Down, Right, L, R before the Takara logo disappears when the game first begins. If entered correctly Terry Bogard will say "OK" to confirm correct code entry.