These secret battles can only be unlocked in Arcade Mode.

Battle	How to Unlock
Secret "Jade" Battle	Get a double flawless victory and perform a fatality on Shang Tsung when battling against him.
Secret "Noob Saibot" Battle	When you see Noob in "The Temple" stage's background win that battle without using the R2 (Block) button.
Secret "Reptile" Battle	On "The Pit 2 (Night)" stage wait until a shadowy figure flies across the moon, then get a double flawless victory and perform a stage fatality.
Secret "Smoke" Battle	On "The Living Forest" stage wait until Smoke appears behind one of the trees. On that moment press Down + Select repeatedly.