We propose an autonomy system to enable an underwater, remotely operated vehicle (ROV) to engage in autonomous inspection of a nuclear reactor pressure vessel. The autonomy system leverages onboard stereo cameras and an inertial measurement unit (IMU) and incorporates vision-based navigation, feedback control, and robust state estimation. We pursue efficient inspection operations through vehicle deployments that minimize transit time between target inspection sites and generate optimal reference ROV trajectories cognizant of the perception and state estimation algorithm performance. We identify challenges that arise in the development of the proposed autonomous system when operating with constrained onboard sensing arising due to limitations imposed by high radiation levels. Preliminary results highlight the performance of the proposed perceptual methodology and the implications of degraded sensing and uninformative environmental conditions.