The lack of generalization capability of behavior prediction models for autonomous vehicles is a crucial concern for safe motion planning. One way to address this is via self-supervised pre-training through masked trajectory prediction. However, the existing models rely on uniform random sampling of tokens, which is sub-optimal because it implies that all components of driving scenes are equally informative. In this paper, to enable more robust representation learning, we introduce a dynamic masked self-distillation approach to identify and utilize informative aspects of the scenes, particularly those corresponding to complex driving behaviors, such as overtaking. Specifically, for targeted sampling, we propose a dynamic method that prioritizes tokens, such as trajectory or lane segments, based on their informativeness. The latter is determined via an auxiliary network that estimates token distributions. Through sampler optimization, more informative tokens are rewarded and selected as visible based on the policy gradient algorithm adopted from reinforcement learning. In addition, we propose a masked self-distillation approach to transfer knowledge from fully visible to masked scene representations. The distillation process not only enriches the semantic information within the visible token set but also progressively refines the sampling process. Further, we use an integrated training regime to enhance the model's ability to learn meaningful representations from informative tokens. Our extensive evaluation on two large-scale trajectory prediction datasets demonstrates the superior performance of the proposed method and its improved prediction robustness across different scenarios.