Photoacoustic tomography (PAT) enables non-invasive cross-sectional imaging of biological tissues, but it fails to map the spatial variation of speed-of-sound (SOS) within tissues. While SOS is intimately linked to density and elastic modulus of tissues, the imaging of SOS distri-bution serves as a complementary imaging modality to PAT. Moreover, an accurate SOS map can be leveraged to correct for PAT image degradation arising from acoustic heterogene-ities. Herein, we propose a novel approach for SOS reconstruction using only PAT imaging modality. Our method is based on photoacoustic reversal beacons (PRBs), which are small light-absorbing targets with strong photoacoustic contrast. We excite and scan a number of PRBs positioned at the periphery of the target, and the generated photoacoustic waves prop-agate through the target from various directions, thereby achieve spatial sampling of the internal SOS. We formulate a linear inverse model for pixel-wise SOS reconstruction and solve it with iterative optimization technique. We validate the feasibility of the proposed method through simulations, phantoms, and ex vivo biological tissue tests. Experimental results demonstrate that our approach can achieve accurate reconstruction of SOS distribu-tion. Leveraging the obtained SOS map, we further demonstrate significantly enhanced PAT image reconstruction with acoustic correction.