This paper presents a robust image-based visual servoing design for a quad-rotor unmanned aerial vehicle performing a visual target-tracking operation in the presence of turbulent wind. Image information is extracted and processed to control the positioning and heading of the aerial vehicle. A novel adaptive non-singular fast terminal sliding mode strategy is introduced to manage the visual servoing error. Unlike other sliding mode methods, the proposed approach diminishes the complexity of the system due to the reduction of its control parameters while providing practical finite-time convergence, robustness against bounded external disturbances and model uncertainties, non-overestimation of the control gains, and chattering attenuation. Furthermore, the stability of the system in closed loop is guaranteed through Lyapunov theory. Finally, simulation results demonstrate the capabilities and performance of such a controller in a high-fidelity scenario using the Robot Operating System and Gazebo frameworks.