This paper explores online stiffness modulation within a single tail stroke for swimming soft robots. Despite advances in stiffening mechanisms, little attention has been given to dynamically adjusting stiffness in real-time, presenting a challenge in developing mechanisms with the requisite bandwidth to match tail actuation. Achieving an optimal balance between thrust and efficiency in swimming soft robots remains elusive, and the paper addresses this challenge by proposing a novel mechanism for independent stiffness control, leveraging fluid-driven stiffening within a patterned pouch. Inspired by fluidic-driven actuation, this approach exhibits high bandwidth and facilitates significant stiffness changes. We perform experiments to demonstrate how this mechanism enhances both thrust and swimming efficiency. The tail actuation and fluid-driven stiffening can be optimized for a specific combination of thrust and efficiency, tailored to the desired maneuver type. The paper further explores the complex interaction between the soft body and surrounding fluid and provides fluid dynamics insights gained from the vortices created during actuation. Through frequency modulation and online stiffening, the study extends the Pareto front of achievable thrust generation and swimming efficiency.