Hyper-parameter tuning (HPT) for deep learning (DL) models is prohibitively expensive. Sequential model-based optimization (SMBO) emerges as the state-of-the-art (SOTA) approach to automatically optimize HPT performance due to its heuristic advantages. Unfortunately, focusing on algorithm optimization rather than a large-scale parallel HPT system, existing SMBO-based approaches still cannot effectively remove their strong sequential nature, posing two performance problems: (1) extremely low tuning speed and (2) sub-optimal model quality. In this paper, we propose FastTuning, a fast, scalable, and generic system aiming at parallelly accelerating SMBO-based HPT for large DL/ML models. The key is to partition the highly complex search space into multiple smaller sub-spaces, each of which is assigned to and optimized by a different tuning worker in parallel. However, determining the right level of resource allocation to strike a balance between quality and cost remains a challenge. To address this, we further propose NIMBLE, a dynamic scheduling strategy that is specially designed for FastTuning, including (1) Dynamic Elimination Algorithm, (2) Sub-space Re-division, and (3) Posterior Information Sharing. Finally, we incorporate 6 SOTAs (i.e., 3 tuning algorithms and 3 parallel tuning tools) into FastTuning. Experimental results, on ResNet18, VGG19, ResNet50, and ResNet152, show that FastTuning can consistently offer much faster tuning speed (up to $80\times$) with better accuracy (up to 4.7% improvement), thereby enabling the application of automatic HPT to real-life DL models.