Magnetic sensing beyond linear regime could broaden the frequency range of detectable magnetic fields, which is crucial to various microwave and quantum applications. Recently, nonlinear interactions in diamond nitrogen-vacancy (NV) centers, one of the most extensively studied quantum magnetic sensors, are proposed to realize magnetic sensing across arbitrary frequencies. In this work, we enhance these capabilities by exploiting the nonlinear spin dynamics in hybrid systems of NV centers and ferri- or ferro-magnetic (FM) thin films. We study the frequency mixing effect in the hybrid NV/magnon systems, and demonstrate that the introduction of FM not only amplifies the intensity of nonlinear resonance signals that are intrinsic to NV spins, but also enables novel frequency mixings through parametric pumping and nonlinear magnon scattering effects. The discovery and understanding of the magnetic nonlinearities in hybrid NV/magnon systems position them as a prime candidate for magnetic sensing with a broad frequency range and high tunablity, particularly meaningful for nanoscale, dynamical, and non-invasive materials characterization.