In this work, we investigate the performance of a hybrid propulsion mechanism for a robotic fish based on the combined bending and flapping motions of a flexible tail with a bio-inspired caudal fin extension. The tail consists of an Aluminum substrate attached to a pair of macro-fiber composite (MFC) piezoelectric laminates and subject to flapping motion actuated by a servomotor. A testing platform, equipped with a distance laser sensor, is developed to measure the produced tail deformation over a range of actuation frequencies and amplitudes of lateral oscillations. The objective is to verify the biomimicry of the system and identify the optimal actuation that maximizes the thrust generation of the propulsive tail. Optimal actuation entails the vibration of the MFC at resonance and utilizing its dynamic model to synchronize its motion with that of a motor to produce a biomimetic motion. Frequency response curves are generated and verified against a model of underwater beam dynamics. The experimental component of the present work also includes the development of a robotic fish prototype that encompasses a main 3d-printed body designed as a streamlined waterproof enclosure of the electronics including a microcontroller, a Raspberry Pi camera module, and a high-voltage amplifier along with a servomotor actuating the bio-inspired tail. The mass distribution of the electronic components is adjusted to ensure the buoyancy of the robotic fish in water. Free-swimming tests of the robot are successfully conducted to demonstrate the performance of the hybrid propulsion mechanism in terms of forward swimming speed and maneuverability. The performance is then compared against other robotic fish works and found to provide a higher propulsion compared to smart material-based designs while also providing a smaller design compared to the motor-based solutions.