In 1-Player mode defeat a Black Digimon when it attacks you and it will become available as a playable character and will be able to digivolve as specified below and have the ability to absorb energy while grabbing the opponent

Unlock BlackGabumon:
In Single-Player mode defeat BlackGabumon during a 'Surprise Attack'. He can digivolve into BlackGarurumon and BlackMetalGarurumon.

Unlock BlackGuilmon:
In Single-Player mode defeat BlackGuilmon during a 'Surprise Attack'. He can digivolve into BlackGrowlmon and ChaosGallantmon.

Unlock BlackAgumon:
In Single-Player mode defeat BlackAgumon during a 'Surprise Attack'. He can digivolve into BackGreymon and BlackWarGreymon.

The following stages become available options when you play through 1-Player mode and complete the corresponding task.

Unlock Ice Palace:
Play through 1-Player mode selecting the easiest match on each stage.

Unlock Chaos Wasteland:
Play through 1-Player mode and beat Neemon, MaloMyotismon, Duskmon, Omnimon, or Diaboromon.

Select the indicated final stage of 1-Player mode and defeat the boss to unlock him.

Unlock Duskmon:
Play through 1-player mode and choose the 2nd final stage down.

Unlock Omnimon:
Play through 1-player mode and choose the 3rd final stage down.

Unlock Diaboromon:
Play through 1-player mode and choose the 4th final stage down.

Unlock Neemon:
Play through 1-player mode and choose the 5th final stage down.

Unlock MaloMyotismon:
Follow the hardest path through the 1-player mode and defeat MaloMyotismon.

One Hit Kill:
At the title screen enter Right, Up, Left, Down, A, L + R.

Evolve Energy Item:
At the title screen enter Y, Right, Down, B, L, A, R, A, Y.

Evolve Meter is Full:
At the title screen enter X, Right, A, Y, Left, B, L + R