Metasurfaces have garnered significant attention for unnatural abilities to modulate waves across various physics domains, including elastics. However, existing elastic metasurfaces are limited to narrowband operations due to chromatic aberrations; moreover, these exhibit highly discrete phase profiles due to the empty spaces required for each meta-atom to function as an individual waveguide. Herein, to address these, we propose a synthesized dispersion engineering that compensates for higher-order wave dispersion, and considers both diffraction and refraction. This approach allows for the design of an elastic metasurface with achromatic focusing capability across an ultrabroadband range, from audible to ultrasound frequencies. By exploiting Kirchhoff-Love plate theory, we demonstrate achromatic focusing with a quasi-continuous phase profile. Additionally, we harness the amplified electrical energy generated by piezoelectric elements attached at the confocal point. Our precise yet straightforward design strategy can be extended to other wave dynamics, including photonics and acoustics, and applied to various scenarios.