This paper addresses the tracking control problem of 3D trajectories for underactuated torpedo-like Autonomous Underwater Vehicles (AUVs). A smooth control scheme is designed, without any a priori knowledge of the AUV model parameters, guaranteeing prescribed performance tracking despite the presence of external disturbances representing ocean currents and waves. This work is the first approach on underactuated systems employing the Prescribed Performance notion, originally proposed in -. Moreover, only the desired trajectory and none of its higher order derivatives is employed in the control scheme. Furthermore, the stability of the unactuated degrees of freedom is secured without incorporating the corresponding measurements in the control signal, thus simplifying implementation and increasing robustness against measurement noises. The proposed control scheme: i) is of low complexity, ii) avoids singularities that arise owing to the error definition in the kinematic model and iii) guarantees, through the appropriate selection of certain performance functions, configuration constraints that may arise owing to the limited field of view of cameras in case a vision based sensor system with on board cameras is adopted. Finally, simulation results clarify and verify the approach.