Duct exploration and maintenance is a task well suited for small agile robots, which must be capable of navigating complex and irregular systems of ducts. Previously, we presented a tensegrity robot, DuCTT (Duct Climbing Tetrahedral Tensegrity), which demonstrated the plausibility of such a robot for duct exploration but was never able to successfully demonstrate climbing. Here we present DuCTTv2, redesigned from the ground up to address issues with actuator power, cable routing, compliance and synchronized control present in our first prototype. These improvements allow the prototype to be the first tensegrity robot to demonstrate duct climbing, and does so with an average climb speed of 1.4 cm/s. We also demonstrate initial tests of the prototypes ability to bend and translate its two segments relative to one another, which will allow it to navigate T-junctions and sharp corners commonly found in duct systems. Testing of the prototype is conducted to demonstrate the new faster and more robust control of motion, and analysis of dynamic simulations is presented.