Equipping unmanned aerial vehicles (UAVs) with bistable robotic grippers allows them to perch on natural and artificial structures, extending mission duration by minimizing energy consumption during stationary operations. However, achieving both compliant triggering and powerful grasping remains a important challenge, particularly in the absence of active actuators. In this work, we present a magnetic tensegrity-enabled robotic gripper (MTRG) with an adaptive energy barrier by leveraging nonlinear interaction forces between magnets. This physical intelligence enables our MTRG to merge both sensitivity and strength, showcasing a failure-to-triggering force ratio exceeding 2 orders of magnitude, which allows for customized responses to varying interaction requirements. This capability involves gentle triggering and robust grasping, analogous to the behavior exhibited by bats. To enable repeated operation, an integrated inflatable airbag is used to reset the bistable system, allowing for multiple grasping behaviors without manual intervention. When integrated into UAVs, MTRGs showcase reliable perching abilities across diverse scenarios, highlighting the potential of passive mechanisms for enhancing the adaptability of energy barriers to achieve long-duration and high-altitude operations.