In this study, we address the challenge of disturbance estimation in legged robots by introducing a novel continuous-time online feedback-based disturbance observer that leverages measurable variables. The distinct feature of our observer is the integration of dynamic gains and comparison functions, which guarantees predefined convergence of the disturbance estimation error, including ultimately uniformly bounded, asymptotic, and exponential convergence, among various types. The properties of dynamic gains and the sufficient conditions for comparison functions are detailed to guide engineers in designing desired convergence behaviors. Notably, the observer functions effectively without the need for upper bound information of the disturbance or its derivative, enhancing its engineering applicability. An experimental example corroborates the theoretical advancements achieved.