Hydrogels’ exceptional mechanical strength and skin-adhesion characteristics offer significant advantages for various applications, particularly in the fields of tissue adhesion and wearable sensors. Herein, we incorporated a combination of metal-coordination and hydrogen-bonding forces in the design of stretchable and adhesive hydrogels. We synthesized four hydrogels, namely PAID-0, PAID-1, PAID-2, and PAID-3, consisting of acrylamide (AAM), N,N′-methylene-bis-acrylamide (MBA), and methacrylic-modified dopamine (DA). The impact of different ratios of iron (III) ions to DA on each hydrogel’s performance was investigated. Our results demonstrate that the incorporation of iron–dopamine complexes significantly enhances the mechanical strength of the hydrogel. Interestingly, as the DA content increased, we observed a continuous and substantial improvement in both the stretchability and skin adhesiveness of the hydrogel. Among the hydrogels tested, PAID-3, which exhibited optimal mechanical properties, was selected for adhesion testing on various materials. Impressively, PAID-3 demonstrated excellent adhesion to diverse materials and, combined with the low cytotoxicity of PAID hydrogel, holds great promise as an innovative option for biomedical engineering applications.