Temporal Graph Neural Networks (TGNNs) have become indispensable for analyzing dynamic graphs in critical applications such as social networks, communication systems, and financial networks. However, the robustness of TGNNs against adversarial attacks, particularly sophisticated attacks that exploit the temporal dimension, remains a significant challenge. Existing attack methods for Spatio-Temporal Dynamic Graphs (STDGs) often rely on simplistic, easily detectable perturbations (e.g., random edge additions/deletions) and fail to strategically target the most influential nodes and edges for maximum impact. We introduce the High Impact Attack (HIA), a novel restricted black-box attack framework specifically designed to overcome these limitations and expose critical vulnerabilities in TGNNs. HIA leverages a data-driven surrogate model to identify structurally important nodes (central to network connectivity) and dynamically important nodes (critical for the graph's temporal evolution). It then employs a hybrid perturbation strategy, combining strategic edge injection (to create misleading connections) and targeted edge deletion (to disrupt essential pathways), maximizing TGNN performance degradation. Importantly, HIA minimizes the number of perturbations to enhance stealth, making it more challenging to detect. Comprehensive experiments on five real-world datasets and four representative TGNN architectures (TGN, JODIE, DySAT, and TGAT) demonstrate that HIA significantly reduces TGNN accuracy on the link prediction task, achieving up to a 35.55% decrease in Mean Reciprocal Rank (MRR) - a substantial improvement over state-of-the-art baselines. These results highlight fundamental vulnerabilities in current STDG models and underscore the urgent need for robust defenses that account for both structural and temporal dynamics.