We perform a general analysis of the long-wavelength mirror instability in multispecies plasmas with generally non-Maxwellian distributions. The general dispersion relation depends on several moments of the distribution function, in addition to the perpendicular and parallel temperature. A most general condition of the mirror instability is derived that is valid for any gyrotropic distribution functions of the plasma species and any number of species. Deviations of the bi-Maxwellian shape may be favorable for the mirror instability but may also suppress it. The resulting effect is rather sensitive to the details of the distribution function.