These characters are unlocked after you beat them in story mode.

Unlockable	How to unlock
Akira Otoishi	Complete Episode 3 of Part 4's story mode.
Cars	Complete Part 2's story mode.
Diavolo	Complete Part 5's story mode.
Dio (Part 3)	Complete Part 3's story mode.
Enrico Pucci	Complete Part 6's story mode.
Esidici	Complete Episode 5 of Part 2's story mode.
Funny Valentine	Complete Part 7's story mode.
Gyro Zeppeli	Complete Episode 1 of Part 7's story mode.
Hol Horse	Complete Episode 6 of Part 3's story mode.
Jean Pierre Polnareff	Complete Episode 3 of Part 3's story mode.
Koichi Hirose	Complete Episode 4 of Part 4's story mode.
Kosaku Kawajiri (Kira)	Complete Part 4's story mode.
Mohammed Advol	Complete Episode 1 of Part 3's story mode.
Narancia Ghirga	Complete Part 5's story mode.
Rohan Kishibe	Complete Episode 6 of Part 4's story mode.
Wham	Complete Episode 3 of Part 2's story mode.