Metasurfaces have attracted widespread attention due to an increasing demand of compact and wearable optical devices. For many applications, polarization-insensitive metasurfaces are highly desirable, and appear to limit the choice of their constituent elements to isotropic nanostructures. This greatly restricts the number of geometric parameters available in design. Here, we demonstrate a polarization-insensitive metalens using otherwise anisotropic nanofins which offer additional control over the dispersion and phase of the output light. As a result, we can render a metalens achromatic and polarization-insensitive across nearly the entire visible spectrum from wavelength λ = 460 nm to 700 nm, while maintaining diffraction-limited performance. The metalens is comprised of just a single layer of TiO2 nanofins and has a numerical aperture of 0.2 with a diameter of 26.4 µm. The generality of our polarization-insensitive design allows it to be implemented in a plethora of other metasurface devices with applications ranging from imaging to virtual/augmented reality.