This paper is devoted to the active turn control of a free-swimming multilink dolphin-like robot, with emphasis on yaw and pitch controls. With full consideration of both mechanical configuration and propulsive principle of the robot consisting of a yaw joint and multiple pitch joints, a viable approach to perform yaw maneuvers via laterally directed biases is formed, providing an advantage in qualitative and quantitative assessment. Meanwhile, based on the feedback of the pitch angle measured by an onboard gyroscope, a closed-loop control strategy in dorsoventral motions is proposed to achieve agile and swift pitch maneuvers. More remarkably, two hybrid acrobatic stunts, i.e., frontflip and backflip, are first implemented on the physical robot. The latest results obtained demonstrate the effectiveness of the proposed methods. It is also confirmed that the dolphin robot achieves better performance for pitch maneuvers than it does for yaw maneuvers, agreeing well with the biological observations.