Autonomous robots can transform how we observe marine ecosystems, but close-range operation in reefs and other cluttered habitats remains difficult. Vehicles must maneuver safely near animals and fragile structures while coping with currents, variable illumination and limited sensing. Previous approaches simplify these problems by leveraging soft materials and bioinspired swimming designs, but such platforms remain limited in terms of deployable autonomy. Here we present a sea turtle-inspired autonomous underwater robot that closed the gap between bioinspired locomotion and field-ready autonomy through a tightly integrated, vision-driven control stack. The robot combines robust depth-heading stabilization with obstacle avoidance and target-centric control, enabling it to track and interact with moving objects in complex terrain. We validate the robot in controlled pool experiments and in a live coral reef exhibit at the New England Aquarium, demonstrating stable operation and reliable tracking of fast-moving marine animals and human divers. To the best of our knowledge, this is the first integrated biomimetic robotic system, combining novel hardware, control, and field experiments, deployed to track and monitor real marine animals in their natural environment. During off-tether experiments, we demonstrate safe navigation around obstacles (91\% success rate in the aquarium exhibit) and introduce a low-compute onboard tracking mode. Together, these results establish a practical route toward soft-rigid hybrid, bioinspired underwater robots capable of minimally disruptive exploration and close-range monitoring in sensitive ecosystems.