Accurate estimation of attitude (pitch, roll) is a prerequisite for ensuring safe navigation during vehicle control execution. In dynamic environments, the presence of acceleration often degrades the accuracy and robustness of attitude estimation using traditional algorithms with Micro-Electro-Mechanical Systems (MEMS) Inertial Measurement Unit (IMU). This paper proposes a robust adaptive error state Kalman filter (RAESKF) algorithm for attitude estimation of MEMS IMU under dynamic acceleration conditions. The RAESKF algorithm decomposes the true attitude Direction Cosine Matrix (DCM) into nominal and error components. An error state Kalman filter is utilized to fuse real-time measurements from MEMS gyroscope and accelerometer, estimating the error component, which is then used to correct the nominal attitude DCM. Furthermore, within the error state Kalman filtering framework, a dynamic acceleration robust adaptive adjustment strategy is implemented. This strategy relies on real-time data monitoring, threshold-based decision-making, and switching mechanisms. It adaptively selects between dynamic acceleration model compensation and online adjustment of the measurement noise covariance matrix. The primary objective of this strategy is to mitigate the impact of disturbance induced by dynamic acceleration on attitude estimation, thereby enhancing the accuracy and robustness. Laboratory rotation experiments have demonstrated that the algorithm improved pitch and roll measurement accuracy by at least 8.81% and 11.69%, respectively, under rotational conditions. In dynamic acceleration conditions, pitch and roll measurement accuracy improved by at least 42.76% and 67.21%, respectively.