Basic Trope: Fugitive must dye their hair to help them evade their pursuers.
Straight: Rachel, forced on the run, dyes her distinctive red hair brown so as to throw off anyone looking for a woman fitting her description.
Hiro and the rest of his party learn that Emperor Evulz has all his forces out searching for them, so they all dye their hair different colors.
Or the same color.
Justified: Alice is dying her hair because she is apart of a witness protection program.
Inverted: As part of an alias she's creating in hopes of catching the eye of her target, Farah dyes her hair a more distinctive shade.
Subverted: Rachel attempts to dye her hair, only to find the coloring doesn't work properly.
Double Subverted: The coloring doesn't work because she was holding the bottle upside down. When she turns it right side up again, the bottle's completely empty.
Parodied: To avoid being noticed, Rachel dyes her distinctive red hair purple. And it works.
Zig Zagged: After learning that the Emperor's forces are looking for them, Hiro and Ichigo refuse to dye their hair, while Kowalski and Lorelai do. Mana isn't certain she wants to, but Kowalski convinces her to after it becomes clear Evulz is specifically searching for her. Eventually, she stops dyeing it after resolving to stop running.
Sharon tries to dye her dark hair a lighter shade... and accidentally bleaches it white.
Played For Drama: Rachel's pursuers have a "shoot on sight" order. She tries altering her appearance; as she's working on her hair, a patrol reaches the door of her hideout and knocks, demanding entry...