Here is a list of characters that can't be unlocked through Story Mode.

Unlockable	How to Unlock
Chopperman	Finish the Thousand Arena One To One in any difficulty with the 45 characters.
Main character support versions	Execute all the character moves in Training mode or finish a Thousand Arena tournament with the wanted character.
Neptune	Connect to the Nintendo WFC and select "Download Content" to unlock a secret level in Story Mode. Finish this level to unlock Neptune.
Shirahoshi	Connect to the Nintendo WFC and select "Download Content" to unlock a secret level in Story Mode. Finish this level to unlock Shirahoshi.
Soldier Docking Emperor	Finish the Thousand Arena Battle Royale in any difficulty with the 45 characters.