Shape memory alloy (SMA) has been widely used in soft robotics systems due to its high work density, shape programmability, rigidity tunability and low requirement of the peripheral electronic devices and power for control and actuation. However, the low bandwith of the SMA actuator resulted in long cooling time that limit the performance of the soft robotics. To address this issue, methods like embedding thermally conductive elastomer and adding antagonistic mechanisms have been attempted. Here, we combine both methods and construct a series of study to characterize the improvement in actuation performance of the SMA actuators both in air and water by embedding the SMA wire inside liquid metal embedded elastomer with various liquid metal volume ratio. The improvement in actuation frequency leads to a locomotion speed improvement of a frog-inspired swimming soft robot.