Cetaceans are very efficient swimmers, with estimated propulsive efficiencies that exceed mechanical propellers. However, experiments to verify these efficiencies have been limited because swimming kinematics and kinetics are difficult to measure due to the inherent challenges of the marine environment. Biologging tags are used to measure kinematic data from a single location on the animal, but information about whole-body kinematics and kinetics is limited. To address this issue, we present an approach to estimate sagittal-plane, whole-body kinematics of a bottlenose dolphin (Tursiops truncatus) from tag data using machine learning techniques. We segment the dolphin body according to a sagittal-plane hydromechanical model of bottlenose dolphin swimming, with a head, torso, and two caudal peduncle segments, to which a flexible, semi-lunate fluke is attached. The goal is to map the kinematics of the torso segment that can be measured using biologging tags to the joint angles of the model. A Temporal Convolutional Network (TCN) was chosen due to its ability to take into account temporal information in a sequence for predictions. To train the TCN, we used synthetic data from the hydromechanical model. Our results show that the TCN was able to learn the mapping from the torso angle to whole-body dynamics (RMSE = 0.097°). When the TCN trained on the synthetic data was then applied to whole-body kinematic data extracted from videos of sagittal-plane swimming, the network made good predictions of the swimming motion, but with higher error (RMSE = 0.376°). This approach will be used to estimate body posture and swimming kinematics of dolphins in both managed and wild settings, greatly expanding our ability to investigate dolphin swimming behavior using biologging tags.