How to unlock alternate costumes for Ryu, Ayane, Kasumi & Momiji. You can only obtain Crystal Skulls on Normal or higher difficulty, also you only need to pick up the Crystal Skull to unlock Ryu & Ayane's 4th costume.

Costume	How to unlock
Kasumi's 3rd costume	Beat 25 Ninja Trials with Kasumi.
Kasumi's 4th costume	Beat 50 Ninja Trials with Kasumi.
Momiji 3rd costume	Beat 25 Ninja Trials with Momiji.
Momiji 4th costume	Beat 50 Ninja Trials with Momiji.
Ryu and Ayane 3rd costume	Collect all 50 scarabs.
Ryu and Ayane 4th costume	Collect all 10 Crystal Skulls.