The imaging of tiny objects within deep-subwavelength ranges is essential for applications such as nondestructive evaluations and sonar systems. To achieve super-resolution imaging, this study proposes a hyper- lens based on a systematically designed hyperbolic acoustic metamaterial (HAMM). A two-step inverse design process is introduced: first, a conceptual HAMM unit cell is generated via topology optimization, followed by fine-tuning of geometrical parameters. Effective material properties are calculated using a field-averaging homogenization method, and the optimized HAMM's characteristics are analyzed through time-harmonic and dispersion analyses. The super-resolution imaging performance of the hyperlens is demonstrated both numerically and experimentally, confirming its ability to overcome the diffraction limit.