The complex dynamics of animal manoeuvrability in the wild is extremely challenging to study. The cheetah (Acinonyx jubatus) is a perfect example: despite great interest in its unmatched speed and manoeuvrability, obtaining complete whole-body motion data from these animals remains an unsolved problem. This is especially difficult in wild cheetahs, where it is essential that the methods used are remote and do not constrain the animal’s motion. In this work, we use data obtained from cheetahs in the wild to present a trajectory optimisation approach for estimating the 3D kinematics and joint torques of subjects remotely. We call this approach kinetic full trajectory estimation (K-FTE). We validate the method on a dataset comprising synchronised video and force plate data. We are able to reconstruct the 3D kinematics with an average reprojection error of 17.69 pixels (62.94% PCK using the nose-to-eye(s) length segment as a threshold), while the estimates produce an average root-mean-square error of 171.3N (~17.16% of peak force during stride) for the estimated ground reaction force when compared against the force plate data. While the joint torques cannot be directly validated against ground truth data, as no such data is available for cheetahs, the estimated torques agree with previous studies of quadrupeds in controlled settings. These results will enable deeper insight into the study of animal locomotion in a more natural environment for both biologists and roboticists.