Inspired by the fastest observed live fishes, we have designed, built and tested a robotic fish that emulates the fast-start maneuver of these fishes and generates acceleration and velocity magnitudes comparable to those of the live fishes within the same time scale. We have designed the robotic fish such that it uses the snap-through bucking of its spine to generate the fast-start response. We have used a dynamic snap-through buckling model and a series of experiments on a beam under snap-through buckling to describe the robotic fish's motion. Our under-actuated robot relies on passive dynamics of a continuous beam to generate organic waveforms. In its transient fast-start maneuver, our robotic fish produces mode shapes very similar to those observed in live fishes, by going through a snap-through bifurcation. We have also used a nonlinear structural model subjected to a non-conservative eccentric compressive force, which is constrained to act tangential to the structure at all times, coupled with a simple fluid dynamic model to approximate the transient behavior of the robot. We relate the numerical results from our nonlinear model to the dynamics observed in the live system proposing an updated kinematic model to understand the mode shapes observed in the fast-start maneuver of the live fishes. We also report on deploying the robotic fish in a river.