Transfer-based targeted adversarial attacks against black-box deep neural networks (DNNs) have been proven to be significantly more challenging than untargeted ones. The impressive transferability of current SOTA, the generative methods, comes at the cost of requiring massive amounts of additional data and time-consuming training for each targeted label. This results in limited efficiency and flexibility, significantly hindering their deployment in practical applications. In this paper, we offer a self-universal perspective that unveils the great yet underexplored potential of input transformations in pursuing this goal. Specifically, transformations universalize gradient-based attacks with intrinsic but overlooked semantics inherent within individual images, exhibiting similar scalability and comparable results to time-consuming learning over massive additional data from diverse classes. We also contribute a surprising empirical insight that one of the most fundamental transformations, simple image scaling, is highly effective, scalable, sufficient, and necessary in enhancing targeted transferability. We further augment simple scaling with orthogonal transformations and block-wise applicability, resulting in the Simple, faSt, Self-universal yet Strong Scale Transformation (S$^4$ST) for self-universal TTA. On the ImageNet-Compatible benchmark dataset, our method achieves a 19.8% improvement in the average targeted transfer success rate against various challenging victim models over existing SOTA transformation methods while only consuming 36% time for attacking. It also outperforms resource-intensive attacks by a large margin in various challenging settings.