Here is the full list of all 12 The Rumble Fish + achievements.
Complete the game without using any continues
Complete arcade mode with Kaya
Complete arcade mode with Boyd
Complete arcade mode with Hikari
Complete arcade mode with Typhon
Complete arcade mode with Viren
Complete arcade mode with Garnet
Complete arcade mode with Orville
Complete arcade mode with Aran
Complete arcade mode with Greed
Complete arcade mode with Zen
Play a VS match