Animals have evolved highly effective locomotion capabilities in terrestrial, aerial, and aquatic environments. Over life's history, mass extinctions have wiped out unique animal species with specialized adaptations, leaving paleontologists to reconstruct their locomotion through fossil analysis. Despite advancements, little is known about how extinct megafauna, such as the Ichthyosauria one of the most successful lineages of marine reptiles, utilized their varied morphologies for swimming. Traditional robotics struggle to mimic extinct locomotion effectively, but the emerging soft robotics field offers a promising alternative to overcome this challenge. This paper aims to bridge this gap by studying Mixosaurus locomotion with soft robotics, combining material modeling and biomechanics in physical experimental validation. Combining a soft body with soft pneumatic actuators, the soft robotic platform described in this study investigates the correlation between asymmetrical fins and buoyancy by recreating the pitch torque generated by extinct swimming animals. We performed a comparative analysis of thrust and torque generated by Carthorhyncus, Utatsusaurus, Mixosaurus, Guizhouichthyosaurus, and Ophthalmosaurus tail fins in a flow tank. Experimental results suggest that the pitch torque on the torso generated by hypocercal fin shapes such as found in model systems of Guizhouichthyosaurus, Mixosaurus and Utatsusaurus produce distinct ventral body pitch effects able to mitigate the animal's non-neutral buoyancy. This body pitch control effect is particularly pronounced in Guizhouichthyosaurus, which results suggest would have been able to generate high ventral pitch torque on the torso to compensate for its positive buoyancy. By contrast, homocercal fin shapes may not have been conducive for such buoyancy compensation, leaving torso pitch control to pectoral fins, for example. Across the range of the actuation frequencies of the caudal fins tested, resulted in oscillatory modes arising, which in turn can affect the for-aft thrust generated.