Recent research has shown the vulnerability of Spiking Neural Networks (SNNs) under adversarial examples that are nearly indistinguishable from clean data in the context of frame-based and event-based information. The majority of these studies are constrained in generating adversarial examples using Backpropagation Through Time (BPTT), a gradient-based method which lacks biological plausibility. In contrast, local learning methods, which relax many of BPTT's constraints, remain under-explored in the context of adversarial attacks. To address this problem, we examine adversarial robustness in SNNs through the framework of four types of training algorithms. We provide an in-depth analysis of the ineffectiveness of gradient-based adversarial attacks to generate adversarial instances in this scenario. To overcome these limitations, we introduce a hybrid adversarial attack paradigm that leverages the transferability of adversarial instances. The proposed hybrid approach demonstrates superior performance, outperforming existing adversarial attack methods. Furthermore, the generalizability of the method is assessed under multi-step adversarial attacks, adversarial attacks in black-box FGSM scenarios, and within the non-spiking domain.