Low-power asymmetric multicore processors (AMPs) attract considerable attention due to their appealing performance-power ratio for energy-constrained environments. However, these processors pose a significant programming challenge due to the integration of cores with different performance capabilities, asking for an asymmetry-aware scheduling solution that carefully distributes the workload. The recent HEVC standard, which offers several high-level parallelization strategies, is an important application that can benefit from an implementation tailored for the low-power AMPs present in many current mobile or hand-held devices. In this scenario, we present an architecture-aware implementation of an HEVC decoder that embeds a criticality-aware scheduling strategy tuned for a Samsung Exynos 5422 system-on-chip furnished with an ARM big.LITTLE AMP. The performance and energy efficiency of our solution is further enhanced by exploiting the NEON vector engine available in the ARM big.LITTLE architecture. Experimental results expose a 1080p real-time HEVC decoding at 24 frames/sec, and a reduction of energy consumption over 20%.