Hydraulically amplified self-healing electrostatic (HASEL) actuators are known for their muscle-like activation, rapid operation, and direct electrical control, making them highly versatile for use in soft robotics. While current methods for enhancing HASEL actuator performance largely emphasize material innovation, our approach offers an additional architectural strategy. In this study, we introduce a novel hydraulically amplified rigidity-adaptive electrostatic (HARIE) actuator designed to significantly enhance HASEL actuator performance while maintaining controllability by elucidating the underlying issues of the pull-in instability. Our experimental results indicate that the HARIE actuator achieves a significant improvement, with over a 200% increase in angular output and consistently strong torque compared with HASEL actuators with flexible electrodes. Notably, the maximum step of the HARIE actuator is 21.8°/kV, approximately one third of that of the HASEL actuator with rigid electrodes (62.3°/kV), suggesting smoother motion control. The HARIE actuator's effectiveness is further demonstrated in practical applications; it successfully grasps an orange weighing 15.2 g and a delicate dandelion. Additionally, the actuator's precise targeting capability is evidenced by its ability to manipulate a laser to induce heat accumulation, leading to the balloon's breakdown, thereby showcasing its high level of controllability. The rigidity-adaptive method mitigates the negative impacts of suboptimal materials and demonstrates the potential for significant enhancement when combined with superior materials.