Obtain the relic in the indicated level to unlock the corresponding costume.

Camouflage: Temple of Khamoon.
Catsuit: Sanctuary of the Scion.
Classic: Lost Valley.
Croft Manor Sport: Athenian Owl from Midas's Palace.
Doppelganger: Natla's Mine.
Golden: Griffin Head from Midas's Palace.
Legend: Mountain Caves.
Scorched Natla: Collect all relics.
Swimsuit from Tomb Raider 2: Great Pyramid.