We investigated the effect of strong turbulence on wavefront sensing and compensation by using an adaptive optics (AO) system for non-cooperative targets. We found that for a non-cooperative target in high scintillation environments beacon anisoplanatism degrades the AO system performance, in addition to the scintillation and branch points. In deep turbulence, a beacon wave from an extended beacon samples different turbulent inhomogeneities and acquires different phase aberrations than a beacon wave from a point reference source. This corrupts the optical field of the beacon wave and degrades the AO performance. To mitigate the effects of beacon anisoplanatism we introduced two approaches. The first method is based on an optimization of the aperture diameter of the illuminating beam to reduce the spot size of the beacon. We found that this approach provides a modest Strehl ratio gain for some range of turbulent conditions. The second method includes an estimate of the Green's function for propagation through turbulence from the phase measurements made with an extended beacon, and the use of the Green's function estimate in the beam control system. We plan to evaluate this method in the future work.