Robots operating in human environments need various skills, like slow and fast walking, turning, side-stepping, and many more. However, building robot controllers that can exhibit such a large range of behaviors is a challenging problem that requires tedious investigation for every task. We present a unified model-based control algorithm for imitating different animal gaits without expensive simulation training or real-world fine-tuning. Our method consists of stance and swing leg controllers using a centroidal dynamics model augmented with online adaptation techniques. We also develop a whole-body trajectory optimization procedure to fix the kinematic infeasibility of the reference animal motions. We demonstrate that our universal data-driven model-based controller can seamlessly imitate various motor skills, including trotting, pacing, turning, and side-stepping. It also shows better tracking capabilities in simulation and the real world against several baselines, including another model-based imitation controller and a learning-based motion imitation technique.