Polar dielectrics with low crystal symmetry and sharp phonon resonances can support hyperbolic shear polaritons, which are highly confined surface modes with frequency-dependent optical axes and asymmetric dissipation features. So far, these modes have been observed only in bulk natural materials at midinfrared frequencies, with properties limited by available crystal geometries and phonon resonance strength. Here, we introduce hyperbolic shear metasurfaces, which are ultrathin engineered surfaces supporting hyperbolic surface modes with symmetry-tailored axial dispersion and loss redistribution that can maximally enhance light-matter interactions. By engineering effective shear phenomena in these engineered surfaces, we demonstrate geometry-controlled, ultraconfined, low-loss hyperbolic surface waves with broadband Purcell enhancements applicable across a broad range of the electromagnetic spectrum.