Audio classifiers frequently face domain shift, when models trained on one dataset lose accuracy on data recorded in acoustically different conditions. Previous Test-Time Adaptation (TTA) research in speech and sound analysis often evaluates models under fixed or mismatched noise settings, that fail to mimic real-world variability. To overcome these limitations, this paper presents DHAuDS (Dynamic and Heterogeneous Audio Domain Shift), a benchmark designed to assess TTA approaches under more realistic and diverse acoustic shifts. DHAuDS comprises four standardized benchmarks: UrbanSound8K-C, SpeechCommandsV2-C, VocalSound-C, and ReefSet-C, each constructed with dynamic corruption severity levels and heterogeneous noise types to simulate authentic audio degradation scenarios. The framework defines 14 evaluation criteria for each benchmark (8 for UrbanSound8K-C), resulting in 50 unrepeated criteria (124 experiments) that collectively enable fair, reproducible, and cross-domain comparison of TTA algorithms. Through the inclusion of dynamic and mixed-domain noise settings, DHAuDS offers a consistent and publicly reproducible testbed to support ongoing studies in robust and adaptive audio modeling.