At the title screen, hold I and press Right, Left 5 times, Down 2 times, Up. If done right, the screen will change from yellow to green.
To fight against the hidden Bosses R.J. Phase and Carlos Krauser, complete either the second singles or tag team tournament on "Hard Mode". Once all the selectable characters have been defeated, a special series of "Lumberjack Death Match" fights will start with R.J. Phase and Carlos Krauser as your final opponents.
You need a multi tap for this to work. At the title screen, on Controller 5, hold Up + Right + I and press Select to cycle through the songs.
At the title screen, select Single or TAG match. Then select "1P vs 2P" and choose your fighters. Now, at the "Round Start" screen, hold Up + II and press I. If done right, the computer will take over.