Human skin perceives physical stimuli applied to the body and mitigates the risk of physical interaction through its soft and resilient mechanical properties. Social robots would benefit from whole-body robotic skin (or tactile sensors) resembling human skin in realizing a safe, intuitive, and contact-rich human-robot interaction. However, existing soft tactile sensors show several drawbacks (complex structure, poor scalability, and fragility), which limit their application in whole-body robotic skin. Here, we introduce biomimetic robotic skin based on hydrogel-elastomer hybrids and tomographic imaging. The developed skin consists of a tough hydrogel and a silicone elastomer forming a skin-inspired multilayer structure, achieving sufficient softness and resilience for protection. The sensor structure can also be easily repaired with adhesives even after severe damage (incision). For multimodal tactile sensation, electrodes and microphones are deployed in the sensor structure to measure local resistance changes and vibration due to touch. The ionic hydrogel layer is deformed owing to an external force, and the resulting local conductivity changes are measured via electrodes. The microphones also detect the vibration generated from touch to determine the location and type of dynamic tactile stimuli. The measurement data are then converted into multimodal tactile information through tomographic imaging and deep neural networks. We further implement a sensorized cosmetic prosthesis, demonstrating that our design could be used to implement deformable or complex-shaped robotic skin.