In this paper, we study the control of an ellipsoid immersed in an infinite volume of ideal fluid. The dynamics of the uncontrolled body are given by Kirchhoff's laws. The control system is underactuated: one control is an acceleration along an axis of the ellipsoid and two are angular accelerations around the other two axes. By adopting a backstepping viewpoint, we prove that the position and the attitude of the solid can be forced to approximately follow any given path, using fast-oscillating controls. Moreover, we prove that the controlled mechanical system (which includes the impulses) is completely controllable in an arbitrary small time.