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Abstract Metasurfaces, the ultra-thin media with extraordinary wavefront modulation ability, have shown great promise for many potential applications. However, most of the existing metasurfaces are limited by narrow-band and strong dispersive modulation, which complicates their real-world applications and, therefore require strict customized dispersion. To address this issue, we report a general methodology for generating ultra-broadband achromatic metasurfaces with prescribed ultra-broadband achromatic properties in a bottom-up inverse-design paradigm. We demonstrate three ultra-broadband functionalities, including acoustic beam deflection, focusing and levitation, with relative bandwidths of 93.3%, 120% and 118.9%, respectively. In addition, we reveal a relationship between broadband achromatic functionality and element dispersion. All metasurface elements have anisotropic and asymmetric geometries with multiple scatterers and local cavities that synthetically support internal resonances, bi-anisotropy and multiple scattering for ultra-broadband customized dispersion. Our study opens new horizons for ultra-broadband highly efficient achromatic functional devices, with promising extension to optical and elastic metamaterials.