The widespread use of publicly available datasets for training machine learning models raises significant concerns about data misuse. Availability attacks have emerged as a means for data owners to safeguard their data by designing imperceptible perturbations that degrade model performance when incorporated into training datasets. However, existing availability attacks are ineffective when only a portion of the data can be perturbed. To address this challenge, we propose a novel availability attack approach termed Parameter Matching Attack (PMA). PMA is the first availability attack capable of causing more than a 30\% performance drop when only a portion of data can be perturbed. PMA optimizes perturbations so that when the model is trained on a mixture of clean and perturbed data, the resulting model will approach a model designed to perform poorly. Experimental results across four datasets demonstrate that PMA outperforms existing methods, achieving significant model performance degradation when a part of the training data is perturbed. Our code is available in the supplementary materials.