We propose a method for estimating the specific differential phase (K_DP) with high spatial resolution from the received differential phase (Ψ_DP) observed by dual-polarization radar and then evaluate the performance of the estimated K_DP. Because Ψ_DP contains noise, its range derivative, K_DP, is prone to significant errors. The proposed method performs scale-adaptive local polynomial fitting, wherein the fitting window is dynamically adjusted based on the magnitude of the K_DP. This adjustment enables high resolution in regions with large K_DP and noise suppression in regions with small K_DP through optimal setting of parameters. The method was applied to Ψ_DP data from both idealized synthetic experiments and actual radar observations. Compared to existing algorithms, the method improved noise suppression in low-K_DP regions while enhancing accuracy in regions exhibiting fine-scale K_DP variation. The good agreement of the results with Ψ_DP in terms of the cumulative phase shift demonstrated a balance between fine-scale accuracy and robustness.