It has been a great challenge to develop robots that are able to perform complex movement patterns with high speed and, simultaneously, high accuracy. Copepods are animals found in freshwater and saltwater habitats that can have extremely fast escape responses when a predator is sensed by performing explosive curved jumps. Here, we present a design and build prototypes of a combustion-driven underwater soft robot, the "copebot", that, like copepods, is able to accurately reach nearby predefined locations in space within a single curved jump. Because of an improved thrust force transmission unit, causing a large initial acceleration peak (850 Bodylength*s-2), the copebot is 8 times faster than previous combustion-driven underwater soft robots, whilst able to perform a complete 360° rotation during the jump. Thrusts generated by the copebot are tested to quantitatively determine the actuation performance, and parametric studies are conducted to investigate the sensitivities of the input parameters to the kinematic performance of the copebot. We demonstrate the utility of our design by building a prototype that rapidly jumps out of the water, accurately lands on its feet on a small platform, wirelessly transmits data, and jumps back into the water. Our copebot design opens the way toward high-performance biomimetic robots for multifunctional applications.