Closeup exploration of underwater life requires new forms of interaction, using biomimetic creatures that are capable of agile swimming maneuvers, equipped with cameras, and supported by remote human operation. Current robotic prototypes do not provide adequate platforms for studying marine life in their natural habitats. This work presents the design, fabrication, control, and oceanic testing of a soft robotic fish that can swim in three dimensions to continuously record the aquatic life it is following or engaging. Using a miniaturized acoustic communication module, a diver can direct the fish by sending commands such as speed, turning angle, and dynamic vertical diving. This work builds on previous generations of robotic fish that were restricted to one plane in shallow water and lacked remote control. Experimental results gathered from tests along coral reefs in the Pacific Ocean show that the robotic fish can successfully navigate around aquatic life at depths ranging from 0 to 18 meters. Furthermore, our robotic fish exhibits a lifelike undulating tail motion enabled by a soft robotic actuator design that can potentially facilitate a more natural integration into the ocean environment. We believe that our study advances beyond what is currently achievable using traditional thruster-based and tethered autonomous underwater vehicles, demonstrating methods that can be used in the future for studying the interactions of aquatic life and ocean dynamics.