Infections caused by bacteria that are resistant to many drugs are a major threat to public health in many countries around the world. Here we demonstrate the creation of heterogeneous catalytic nanomaterials with outstanding antimicrobial properties against several superbugs. We have shown that replacing a small amount of copper in a generated copper-phosphate-enzyme nanoflower hybrid with silver drastically increases the antimicrobial capacity of the nanomaterial. In this sense, it has been confirmed that the exchange generated silver phosphate nanoparticles on the Cu nanoflowers, with control of the nanoparticle diameter size. The Fenton catalytic activity of the Ag-containing nanobiohybrids was affected, showing better performance with lower amounts of silver in the final hybrid. This effect was confirmed by their antimicrobial efficacy against Escherichia coli, where the Ag4Cu32@CALB hybrid displayed a log reduction of 3.9, an efficiency more than 5000 times higher than that obtained with copper nanoflowers (Cu36@CALB). The hybrid also showed excellent efficacy against other bacteria such as Klebsiella pneumoniae, Pseudomonas aeruginosa, and Mycobacterium smegmatis with log reductions of 7.6, 4.3, and 1.8, respectively.