<p>Achromatic acoustic metasurfaces overcome conventional narrowband limitations for broadband wavefront control yet encounter inherent conflicts between propagation-phase modulation’s inability to deliver required nonlinear compensation and resonant-phase units’ intrinsically narrow bandwidths. Furthermore, achieving high three-dimensional (3D) focusing gain with large numerical aperture necessitates large-scale metasurfaces comprising dispersion-engineered units. To address these challenges, we propose an inverse design framework based on an improved genetic algorithm (GA) to synthesize unit configurations that integrate both propagation and resonance phase mechanisms. The optimized metasurface units enable precise broadband manipulation of transmission phases and amplitudes, thereby maintaining a linear, dispersion-free phase gradient between adjacent units. This framework also establishes a rigorous sub-wavelength design methodology and analyzes the inherent trade-offs among broadband performance, high efficiency, and large numerical aperture. By integrating topology optimization with electro-acoustic analogies, the design systematically tailors the geometrical and effective material properties of metasurface units to achieve desired acoustic functionalities, which highlights the geometric robustness of the optimized topologies. The proposed achromatic metasurface composed of 28 distinct metasurface units can achieve achromatic acoustic focusing within the range of [1.5 kHz, 3.1 kHz] with a relative bandwidth of 69.6% and the numerical aperture (NA) of 0.86. A comprehensive analysis is conducted to investigate the broadband acoustic impedance tuning capabilities of simplified metasurface units, along with an evaluation of the effects of acoustic losses on wave manipulation performance. Finally, experimental validation of the full-scale achromatic metasurface confirms its capabilities of broadband focusing and high focusing gain.</p>