Metasurface lenses, namely metalenses, are ultrathin planar nanostructures that are capable of manipulating the properties of incoming light and imparting lens-like wavefront to the output. Although they have shown promising potentials for the future miniaturization of optics, the chromatic aberration inherited from their diffractive nature plagues them towards many practical applications. Current solutions for creating achromatic metalenses usually require searching through a large number of meta-atoms to find designs that fulfill not only phase but phase dispersion requirements, which leads to intensive design efforts. Besides, most designs are based on regular-shaped antennas driven by the designers intuition and experience, hence only cover a limited design space. Here, we present an inverse design approach that efficiently produces meta-atoms with unintuitive geometries required for broadband achromatic metalenses. We restricted the generated shapes to hold four-fold reflectional symmetry so that the resulting metalenses are polarization insensitive. In addition, meta-atoms generated by our method inheritably have round edges and corners, which make them nanofabrication-friendly. Our experimental characterization shows that our metalenses exhibit superior performance over a broad bandwidth of 465 nm in the near-infrared regime. Our method offers a fast and efficient way of designing high-performance achromatic metalenses and sheds new insights for unintuitive design of other metaphotonic devices.