Strong coupling between single qubits is crucial for quantum information science and quantum computation. However, it is still challenged, especially for single solid-state qubit. Here, we propose a hybrid quantum system, consisting of a coplanar waveguide (CPW) resonator weakly coupled to a single nitrogen-vacancy (NV) spin in diamond and an yttrium-iron-garnet (YIG) nanosphere holding Kerr magnons, to realize strong long-distance spin-spin coupling. With a strong driving field on magnons, the Kerr effect can squeeze magnons, and thus the coupling between the CPW resonator and the squeezed magnons is exponentially enhanced, which produces two cavity-magnon polaritons, i.e., the high-frequency polariton (HP) and the low-frequency polariton (LP). When the enhanced cavity-magnon coupling approaches the critical value (i.e., the frequency of the LP becomes zero), the spin is fully decoupled from the HP, while the coupling between the spin and the LP is significantly improved. In the dispersive regime, a strong spin-spin coupling mediated by the LP is achieved with accessible parameters. Our proposal indicates that the critical cavity-magnon polariton is a potential interface to realize strong spin-spin coupling and manipulates remote solid spins.