This paper describes RoboTerp, a quadrupedal amphibious robot that achieves locomotion on land and in water with the same legs by switching gaits to match the terrain. The central idea hinges on a passive compliant mechanism attached to the lower leg that enables it to behave like a valve during movement in water. The direction of this valve-like mechanism is aligned such that rhythmic oscillations of the legs generate a net thrust that propels the robot forward in water. By design, this oscillatory leg movement achieves splash-free swimming, and thereby overcomes the shortcomings of most previous wheel-leg based designs, in which rotational movement causes water splashing that leads to significant turbulence in the robot surroundings. We examined different materials and morphological parameters to select the best flap configuration. A modular design allowed rapid iterations of these experiments. We confirmed the performance of the best few configurations found during the experiments through fluid simulations. Finally, we report successful demonstrations of RoboTerp walking on asphalt land, swimming in a pool, and transitioning between uneven rock surface and water in an outdoor creek.