This article deals with the recursive filtering issue for a class of nonlinear complex networks (CNs) with switching topologies, random sensor failures and dynamic event-triggered mechanisms. A Markov chain is utilized to characterize the switching behavior of the network topology. The phenomenon of sensor failures occurs in a random way governed by a set of stochastic variables obeying certain probability distributions. In order to save communication cost, a dynamic event-triggered transmission protocol is introduced into the transmission channel from the sensors to the recursive filters. The objective of the addressed problem is to design a set of dynamic event-triggered filters for the underlying CN with a certain guaranteed upper bound (on the filtering error covariance) that is then locally minimized. By employing the induction method, an upper bound is first obtained on the filtering error covariance and subsequently minimized by properly designing the filter parameters. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed filtering scheme.