Recent developments in DNN-based image watermarking techniques have achieved impressive results in protecting digital content. However, most existing methods are constrained to low-resolution images as they need to encode the entire image, leading to prohibitive memory and computational costs when applied to high-resolution images. Moreover, they lack robustness to distortions prevalent in large-image transmission, such as extreme scaling and random cropping. To address these issues, we propose a novel watermarking method based on implicit neural representations (INRs). Leveraging the properties of INRs, our method employs resolution-independent coordinate sampling mechanism to generate watermarks pixel-wise, achieving ultra-high resolution watermark generation with fixed and limited memory and computational resources. This design ensures strong robustness in watermark extraction, even under extreme cropping and scaling distortions. Additionally, we introduce a hierarchical multi-scale coordinate embedding and a low-rank watermark injection strategy to ensure high-quality watermark generation and robust decoding. Experimental results demonstrate that our method significantly outperforms existing schemes in terms of both robustness and computational efficiency while preserving high image quality. Our approach achieves an accuracy greater than 98\% in watermark extraction with only 0.4\% of the image area in 2K images. These results highlight the effectiveness of our method, making it a promising solution for large-scale and high-resolution image watermarking applications.