Temporal Knowledge Graph Alignment (TKGA) seeks to identify equivalent entities across heterogeneous temporal knowledge graphs (TKGs) for fusion to improve their completeness. Although some approaches have been proposed to tackle this task, most assume unified temporal element standards and simplified temporal structures across different TKGs. They cannot deal with TKGA in the wild (TKGA-Wild), where multi-scale temporal element entanglement and cross-source temporal structural imbalances are common. To bridge this gap, we study the task of TKGA-Wild and propose HyDRA, a new and effective solution. HyDRA is the first to reformulate the task via multi-scale hypergraph retrieval-augmented generation to address the challenges of TKGA-Wild.In addition, we design a new scale-weave synergy mechanism for HyDRA, which incorporates intra-scale interactions and cross-scale conflict detection. This mechanism is designed to alleviate the fragmentation caused by multi-source temporal incompleteness and resolves inconsistencies arising from complex and uneven temporal event density distributions, thereby enhancing the model capacity to handle the intricacies of real-world temporal alignment. Finally, there is no standard benchmark that captures these challenges of TKGA-Wild and effectively evaluates existing methods. To this end, we formally propose to benchmark challenges for TKGA-Wild and validate the effectiveness of the method by establishing two new datasets(BETA and WildBETA). Extensive experiments on the new datasets and six representative benchmarks show that BETA and WildBETA better reflect real-world challenges. Meanwhile, HyDRA proposes a new paradigm for TKGA-Wild, consistently outperforming 24 competitive baselines, while maintaining strong efficiency and scalability.