The following costumes become available options when you complete the indicated mission.

Unlock Kankuro's Later Costume:
Complete 'Gaara Returns' (Flashback Mission: Sasuke Chase Arc)

Unlock Temari's Later Costume:
Complete 'Gaara Returns' (Flashback Mission: Sasuke Chase Arc)

Unlock Gaara's Later Costume:
Complete 'Gaara Returns' (Flashback Mission: Sasuke Chase Arc)

Unlock Sasuke Uchiha's Black Costume:
Complete 'Sasuke and Gaara' (Flashback Mission: Leaf Destruction Arc)

Unlock Shikamaru Nara's Chunin Costume:
Complete 'Shikamaru's Squad Is Summoned' (Flashback Mission: Sasuke Chase Arc)

Complete the indicated task to unlock the corresponding character in the game.

Unlock Kakashi Hatake:
Clear Genin Training Arc

Unlock Jiraiya.
Clear 'A Match with Pervy Sage'

Unlock Itachi Uchiha:
Clear 'Fatal Encounter' (Flashback Mission: Tsunade Search Arc)

Unlock Kankuro:
Clear 'The Aburame Clan' (Flashback Mission: Leaf Destruction Arc)

Unlock Gaara:
Clear 'Burning Will of Fire' (Flashback Mission: Leaf Destruction Arc)

Unlock The Third Hokage:
Clear 'Unprecedented Mega Battle' (Flashback Mission: Leaf Destruction Arc)

Unlock Rock Lee: Eight Gates Mode:
Clear 'A Duel that risks their Bond' (Flashback Mission: Sasuke Chase Arc)

Unlock Kimimaro:
Clear 'Battle with the Sound Beguns' (Flashback Mission: Sasuke Chase Arc)

Unlock Kisame Hoshigaki:
Clear 'Toad Sage shows his Ability' (Flashback Mission: Tsunade Search Arc)

Unlock Might Guy:
Clear 'Odd Beast Battles a Scourge' (Flashback Mission: Tsunade Search Arc)

Unlock Orochimaru:
Clear 'Sannin Rock Heaven and Earth' (Flashback Mission: Tsunade Search Arc)

Unlock Kabuto Yakushi:
Clear 'A Whirling Rasengan Explodes' (Flashback Mission: Tsunade Search Arc)

Unlock Temari:
Clear 'The Chunin Exam Sleeper Pick' (Flashback Mission: Leaf Destruction Arc)

Unlock Tsunade:
Clear 'Tsunade finally opens her Eyes' (Flashback Mission: Tsunade Search Arc)

Unlock Sasuke Uchiha - Curse Marked Second State Mode:
Clear 'A Duel that risks their Bond' (Flashback Mission: Sasuke Chase Arc)

Unlock Kimimaro - Curse Marked Second State Mode:
Clear 'A Duel that risks their Bond' (Flashback Mission: Sasuke Chase Arc)

Unlock Naruto Uzumaki - Nine-Tailed Fox Mode:
Clear 'A Duel that risks their Bond' (Flashback Mission: Sasuke Chase Arc)

Unlock Might Guy - Eight Gates Mode:
Clear 'A Duel that risks their Bond' (Flashback Mission: Sasuke Chase Arc)