Agility and trajectory control are two desirable features for robotics, but they become very challenging for soft robots without rigid structures to support rapid manipulations. Here, a curved piezoelectric thin film driven at its structural resonant frequency is used as the main body of an insect-scale soft robot for its fast translational movements, and two electrostatic footpads are used for its swift rotational motions. These two schemes are simultaneously executed during operations through a simple two-wire connection arrangement. A high relative centripetal acceleration of 28 body length per square second compared with existing robots is realized on a 65-milligram tethered prototype, which is better than those of common insects, including the cockroach. The trajectory manipulation demonstration is accomplished by navigating the robot to pass through a 120-centimeter-long track in a maze within 5.6 seconds. One potential application is presented by carrying a 180-milligram on-board sensor to record a gas concentration route map and to identify the location of the leakage source. The radically simplified analog motion adjustment technique enables the scale-up construction of a 240-milligram untethered robot. Equipped with a payload of 1660 milligrams to include the control circuit, a battery, and photoresistors, the untethered prototype can follow a designated, 27.9-centimeter-long “S”-shaped path in 36.9 seconds. These results validate key performance attributes in achieving both high mobility and agility to emulate living agile insects for the advancements of soft robots.