The expansion of human activities at sea is due to the development of ocean exploration and data collection technology. Conventional robots consisting of rigid components play a crucial role in marine applications for their controllability of precision and power. However, these "hard" robots are generally crafted of materials with water-mismatched acoustic impedance, severely limiting their underwater operating capabilities, especially operating in complex ocean environments. Therefore, flexible and acoustically transparent soft robots show great prospects for applications in marine exploration. Transparency is a surprisingly effective approach of camouflage that has been widely adopted by natural animals. Acoustic transparency allows for passive camouflage, enabling robots to blend into the environmental background acoustic field with the advantage of imperceptible motions. Nature has offered us a solution in which an organism possesses both superior body flexibility and near-water acoustic impedance. The jellyfish's highly efficient motion and flexible, gelatinous body have made it an excellent candidate for underwater robot design. Jellyfish possess exceptional underwater capabilities as nearly 95% of it is made of water: the extremely low Young's modulus of jellyfish tissues allows for larger deformation under the same driving force than commonly used metals and elastomers; the near-water density and sound velocity of jellyfish tissues allow for a near-water acoustic impedance, making it difficult for underwater sonic detection. Inspired by this, hydrogel was chosen to be the main design material for our robot. Here, we propose a hydraulically actuated bioinspired hydrogel (HABH) jellyfish to achieve mechanical flexibility and omnidirectional acoustic transparency. The acoustic backscattered energy of the hydrogel jellyfish is reduced to about 1/270 compared to conventional underwater robots, achieving omnidirectional transparency under broadband acoustic detection from 10 kHz to 1MHz. Moreover, the body length of hydrogel jellyfish can contract to about 1/3 of its original length under hydraulic control, exhibiting flexible motion to pass through narrow orifices. This will have tremendous potential to explore and monitor fragile marine ecosystem, minimizing the risk of damage to their surroundings. This novel design of HABH breaks the previous boundaries of underwater robots being either easily acoustically detectable or stiff.