Fiber-optic distributed acoustic sensing (DAS) has proven to be a revolutionary technology for the detection of seismic and acoustic waves with ultralarge scale and ultrahigh sensitivity, and is widely used in oil/gas industry and intrusion monitoring. Nowadays, the single-frequency laser source in DAS becomes one of the bottlenecks limiting its advance. Here, we report a dual-comb-based coherently parallel DAS concept, enabling linear superposition of sensing signals scaling with the comb-line number to result in unprecedented sensitivity enhancement, straightforward fading suppression, and high-power Brillouin-free transmission that can extend the detection distance considerably. Leveraging 10-line comb pairs, a world-class detection limit of 560 fε/√Hz@1 kHz with 5 m spatial resolution is achieved. Such a combination of dual-comb metrology and DAS technology may open an era of extremely sensitive DAS at the fε/√Hz level, leading to the creation of next-generation distributed geophones and sonars.