Atmospheric dynamics, such as turbulence or buoyancy waves, modulate the quiescent refractive index and cause radio-wave scattering during occultations of spacecraft by planetary atmospheres. The resulting rapid signal fluctuations are a common feature observed during occultation experiments, especially in the outer solar system, and provide an opportunity for remote sensing of the underlying atmospheric dynamics. However, the absence of a theory that accounts for strong scattering during atmospheric occultations has obstructed progress in this area, and has restricted data interpretation to the weak-scattering regime. We have removed this limitation of the theory by deriving a formula for the spatial spectrum of intensity fluctuations due to strong scattering in the occultation geometry. In obtaining this new result, we generalized an existing formula for strong scattering from an irregular thin screen to include the effect of a spatially varying average refractive index in the scattering region. In the model phase screen, the refractive irregularities are anisotropic with a size distribution that follows a power law. The strength, axial ratio, orientation, and power-law exponent which characterize the irregularities, as well as the scale height and radius of curvature of the background refractive index, are included in the theoretical expression as free parameters. Unfortunately, the final result takes the form of an intractable double integral. To obtain specific results for the theoretical intensity spectrum, we developed an accurate algorithm for numerical integration. Representative results are given, showing the dependence of the spectrum on each of the free parameters.