Unlock Cronos:
Beat the game two times to unlock Cronos.

Unlock Ganesha:
Beat the game one time to unlock Ganesha.

Unlock Kohryu:
Win four consecutive rounds in Arcade mode. You will fight Kohryu in the next round. Beat him, then complete Arcade mode to unlock Kohryu.

Fight against Uranus:
Beat the game three times to enable Uranus.

Unlock Uranus:
Beat Uranus in stage 16 of Survival mode.

Movie player:
Beat the game once.

Com Battle:
Beat the game twice.

Kid mode:
Beat the game three times.

Big kid mode:
Beat the game four times.

Super buff (DK) mode:
Beat the game five times.

No walls mode:
Beat the game six times.

Weak walls mode:
Beat the game seven times.

Break walls only in final round:
Beat the game eight times.

Slow motion mode:
Beat the game nine times.

High Speed mode:
Beat the game ten times.

No blocking mode:
Beat the game eleven times.

Expert mode:
Beat the game twelve times.

Knock down battle mode:
Beat the game thirteen times.

Human mode:
Beat the game fourteen times

Beast mode:
Beat the game fifteen times.

Hyper mode:
Beat the game sixteen times. Note: This also unlocks Kohryu the Iron Mole.

Thanks to Revolution readers rafael moriel and Andy!