In this work, we study the validated evaluation of two classes of polygamma functions. To achieve fast evaluation of high accuracy, we compare various expansion methods endowed with approximation error bounds and try to find the optimal approximation methods for different domains of real arguments of polygamma functions in terms of computation accuracy and speed. Especially whenever the real agruments of trigamma and tetragamma functions lie in the domain $(0,1]$, it is a bit problematic to achieve a good approximation with reasonable relative errors by directly using various approximation methods. To improve, we apply a combination of the recurrence relations of polygamma functions and asymptotic expansions to achieve a better evaluation with much higher accuracy. Further, we apply the technique of chains of recurrences to speed up the evaluation speed and thus improve the efficiency of the evaluation. The experiments show the efficiency of this work.