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Ultrasound computed tomography (UCT) shows significant promise for imaging the internal structures of soft-tissue organs such as the breast, in particular, the distribution of the important biomarker speed of sound (SoS). Ultrasonic attenuation also represents a potentially highly informative biomarker relevant to disease classification, but it has been extremely difficult to reconstruct reliable images of this property due to the highly aberrating nature of breast tissue coupled with the phase-sensitive nature of the conventional piezoelectric detectors deployed in UCT systems. This study reports on the essential properties of a large-area (LA) phase-insensitive detector, which exploits the pyroelectric effect within membranes of polyvinylidene fluoride (PVDF) and makes the detectors particularly appropriate for quantitative imaging of soft tissue ultrasonic attenuation. These properties include a broad directional response (DR) that is dependent on the frequency content of the incident acoustic radiation but can be flat (±1 dB) out to an angle of incidence of at least ±60°, determined at 3.2 MHz. The thermal origin of the signals generated means that they can be influenced by extraneous background acoustic and vibration noise, and a differential sensor design is presented and modeled which is shown to significantly enhance signal-to-noise ratio for small signal retrieval whilst also contributing to the omnidirectionality. Finally, the high sensitivity of the developed detector and instrumentation combination is demonstrated which enables time-averaged acoustic powers of around several milliwatts to be measured, generated by estimated temperature increases immediately adjacent to the PVDF membrane of a few mK.