Hyperbolic metamaterials, the highly anisotropic subwavelength media, immensely widen the engineering feasibilities for wave manipulation. However, limited by the empirical structural topologies, the reported hyperbolic elastic metamaterials (HEMMs) suffer from the limitations of the relatively narrow frequency width, inflexible adjustable operating subwavelength scale and difficulty to further improve the imaging resolution. Here, we show an inverse-design strategy for HEMMs by topology optimization. We design broadband single-phase HEMMs supporting multipolar resonances at different prescribed deep-subwavelength scales, and demonstrate the super-resolution imaging for longitudinal waves. Benefiting from the extreme enhancement of the evanescent waves, an optimized HEMM at an ultra-low frequency can yield an imaging resolution of ~λ/64, representing the record in the field of elastic metamaterials. The present research provides a novel and general design methodology for exploring the HEMMs with unrevealed mechanisms and guides the ultrasonography and general biomedical applications.