Do the following tasks to unlock the stated characters.

Character	How to unlock
Ace	Complete the Story Mode with two different characters.
Blackbeard	Complete the Story Mode with Shanks.
Crocodile	Complete the Story Mode with three different characters.
Ener	Complete the Story Mode with five different characters.
Mihawk	Complete the Story Mode with all other characters.
Shanks	Complete the Story Mode with Mihawk.
Smoker	Complete the Story Mode with one character.
Vivi	Complete the Story Mode with four different characters.