In this paper, we propose a hyperparameter-specialized adaptive fingerprinting framework named AdaParse for model reverse engineering, which aims at predicting hyperparameters of interest in generative models from the given AI-generated images. Existing methods rely on a single coarse model fingerprint that is originally designed for model-level attribution, which makes it difficult to distinguish fine-grained traces corresponding to different hyperparameter configurations in a multitude of generative models. To address this, our AdaParse dynamically responds to instance-level variations by estimating hyperparameter-specific fingerprints via personalizing estimation networks tailored for each input image. Specifically, our approach simultaneously learns two-branch hypernetworks that balance instance-aware and model-agnostic prior knowledge for fingerprint generation. To enable efficient network personalization, we further propose a Broadcasted Fusion module that transforms condensed feature codes into adaptive parameters through factorized weight generation with enhanced representative capacity. Extensive experiments on the large-scale public dataset across 123 generative models demonstrate that our approach outperforms previous state-of-the-art methods. Code available at https://github.com/lizhuoxun/AdaParse/.