Survival mode - Read the monument on the last island to unlock Survival mode.

Bonus characters - Successfully complete the indicated task to unlock the corresponding character in Versus mode:

Aokiji: Defeat Aokiji on the Normal difficulty.
Arlong: Defeat Arlong in Survival mode.

Enel: Defeat Enel on the Normal difficulty.
Evil Guardian: Defeat Evil Guardian in Survival mode.

Krieg: Defeat Krieg on the Normal difficulty.
Kuma: Defeat Kuma on the Hard difficulty.
Kuro: Defeat Kuro on the Normal difficulty.

Monster Point Chopper: Defeat Monster Point Chopper in Survival mode.
Moria: Defeat Moria on the Normal difficulty.

Nightmare Luffy: Have an axe on Island 1. Use the cannon on Sunny, and shoot yourself to the center of the peak. Find four stairs on the right, and use them to go up. There are three bamboo trees on the right-hand side. Dig there to find the treasure chest that unlocks Nightmare Luffy. Alternately, defeat Nightmare Luffy in Survival mode.

Spandam: Defeat Spandam on the Normal difficulty.

Wapul: Defeat Wapul on the Normal difficulty.

Final Boss: Defeat the final Boss on the Hard difficulty.