The concept of aerial-aquatic robots has emerged as an innovative solution that can operate both in the air and underwater. Previous research on the design of such robots has been mainly focused on mature technologies such as fixed-wing and multi-rotor aircraft. Flying fish, a unique aerial-aquatic animal that can both swim in water and glide over the sea surface, has not been fully explored as a bionic robot model, especially regarding its motion patterns with the collapsible pectoral fins. To verify the contribution of the collapsible wings to the flying fish motion pattern, we have designed a novel bio-robot with collapsible wings inspired by the flying fish. The bionic prototype has been successfully designed and fabricated, incorporating collapsible wings with soft hydraulic actuators, an innovative application of soft actuators to a micro aquatic-aerial robot. We have analyzed and built a precise model of dynamics for control, and tested both the soft hydraulic actuators and detailed aerodynamic coefficients. To further verify the feasibility of collapsible wings, we conducted simulations in different situations such as discharge angles, the area of collapsible wings, and the advantages of using ground effect. The results confirm the control of the collapsible wings and demonstrate the unique multi-modal motion pattern between water and air. Overall, our research represents the study of the collapsible wings in aquatic-aerial robots and significant contributes to the development of aquatic-aerial robots. The using of the collapsible wings must a contribution to the future aquatic-aerial robot.