This study investigates the use of hypercomplex neural networks (HNNs) for balancing control of a four-legged robot. HNNs use advanced mathematical constructs to capture multidimensional data and model the complex dynamics of legged locomotion. Imitation learning is used to train a neural network-based controller to mimic a quadratic programming-based controller for balancing the four-legged robot while standing on two legs. A comparative analysis between traditional neural networks and HNNs is performed to develop a more robust controller for balancing on two legs. The quaternion-based representation effectively handles multidimensional data, allowing for more accurate and robust control of balancing while reducing the number of trainable parameters required.