Silent underwater actuation and object detection are desired for certain applications in environmental monitoring. However, several challenges need to be faced when addressing simultaneously the issues of actuation and object detection using vision system. This paper presents a swimming underwater soft robot inspired by the moon jellyfish (Aurelia aurita) species and other similar robots; however, this robot uniquely utilizes novel artificial muscles and incorporates camera for visual information processing. The actuation characteristics of the novel artificial muscles in water are presented which can be used for any other applications. The bio-inspired robot, Jelly-Z, has the following characteristics: (1) The integration of three 60 mm-long twisted, and coiled polymer fishing line (TCPFL) muscles in a silicone bell to achieve contraction and expansion motions for swimming; (2) A Jevois camera is mounted on Jelly-Z to perform object detection while swimming using a pre-trained neural network; (3) Jelly-Z weighs a total of 215 g with all its components and is capable of swimming 360 mm in 63 seconds. The present work shows, for the first time, the integration of camera detection and TCPFL actuators in an underwater soft jellyfish robot, and the associated performance characteristics. This kind of robot can be a good platform for monitoring of aquatic environment either for detection of objects by estimating the percentage of similarity to pre-trained network or by mounting sensors to monitor water quality when fully developed.