This paper presents SCALER, a versatile free-climbing multi-limbed robot that is designed to achieve tightly coupled simultaneous locomotion and dexterous grasping. Although existing quadruped-limbed robots have shown impressive dexterous skills such as object manipulation, it is essential to balance power-intensive locomotion and dexterous grasping capabilities. We design a torso linkage and a parallel-serial limb to meet such conflicting skills that pose unique challenges in the hardware designs. SCALER employs underactuated two-fingered GOAT grippers that can mechanically adapt and offer 7 modes of grasping, enabling SCALER to traverse extreme terrains with multi-modal grasping strategies. We study the whole-body approach, where SCALER uses its body and limbs to generate additional forces for stable grasping with environments, further enhancing versatility. Furthermore, we improve the GOAT gripper actuation speed to realize more dynamic climbing in a closed-loop control fashion. With these proposed technologies, SCALER can traverse vertical, overhang, upside-down, slippery terrains, and bouldering walls with non-convex-shaped climbing holds under the Earth's gravity.