We present a simple two-step method to fabricate dual-scale superhydrophobic surfaces by using replica molding of poly(dimethylsiloxane) (PDMS) micropillars, followed by deposition of a thin, hard coating layer of a SiO(x)-incorporated diamond-like carbon (DLC). The resulting surface consists of microscale PDMS pillars covered by nanoscale wrinkles that are induced by residual compressive stress of the DLC coating and a difference in elastic moduli between DLC and PDMS without any external stretching or thermal contraction on the PDMS substrate. We show that the surface exhibits superhydrophobic properties with a static contact angle over 160 degrees for micropillar spacing ratios (interpillar gap divided by diameter) less than 4. A transition of the wetting angle to approximately 130 degrees occurs for larger spacing ratios, changing the wetting from a Cassie-Cassie state (C(m)-C(n)) to a Wenzel-Cassie state (W(m)-C(n)), where m and n denote micro- and nanoscale roughness, respectively. The robust superhydrophobicity of the Cassie-Cassie state is attributed to stability of the Cassie state on the nanoscale wrinkle structures of the hydrophobic DLC coating, which is further explained by a simple mathematical theory on wetting states with decoupling of nano- and microscale roughness in dual scale structures.