Most robots operate either exclusively on land or in water. Toward building an amphibious legged robot, we present a morphing limb that can adapt its structure and stiffness for amphibious operation. We draw inspiration for the limb's design from the morphologies of sea turtle flippers and land-faring tortoise legs. Turtles and tortoises have rigid hulls that can be emulated in amphibious robots to provide a convenient, protected volume for motors, electronics, power supply, and payloads. Each of these animals' limbs are tailored for locomotion in their respective environments. A sea turtle flipper has a streamlined profile to reduce drag, making it apt for swimming. A land tortoise leg boasts a strong, expanded cross-section conducive to load-bearing. We capture the morphological advantages of both animals' limbs in our morphing limb via a variable stiffness composite coupled to a pneumatic actuator system that enables on-demand transitions between leg and flipper configurations. We control the degree of stiffness of the limb by varying electrical input to flexible heaters bound to the thermally responsive variable stiffness composite. The proposed morphing amphibious limb design is promising for enabling the next generation of hybrid soft-rigid robots to adapt to unstructured environments.