An important problem in evolution is identifying the genetic basis of how different species adapt to similar environments. Understanding how diverse bacterial pathogens evolve in response to an antimicrobial treatment is a pressing example of this problem, where discovery of molecular parallelism could lead to clinically useful predictions. Evolution experiments with pathogens in environments containing antibiotics, combined with periodic whole population genome sequencing, can be used to identify many contending routes to antimicrobial resistance. We separately propagated two clinically relevant Gram-negative pathogens, Pseudomonas aeruginosa and Acinetobacter baumannii, in increasing concentrations of tobramycin in two different environments each: planktonic and biofilm. Independent of the pathogen, populations adapted to tobramycin selection by parallel evolution of mutations in fusA1, encoding elongation factor G, and ptsP, encoding phosphoenolpyruvate phosphotransferase. As neither gene is a direct target of this aminoglycoside, both are unexpected and underreported causes of resistance. Additionally, both species acquired antibiotic-associated mutations that were more prevalent in the biofilm lifestyle than planktonic, in electron transport chain components in A. baumannii and LPS biosynthesis enzymes in P. aeruginosa populations. Using existing databases, we discovered both fusA1 and ptsP mutations to be prevalent in antibiotic resistant clinical isolates. Additionally, we report site-specific parallelism of fusA1 mutations that extend across several bacterial phyla. This study suggests that strong selective pressures such as antibiotic treatment may result in high levels of predictability in molecular targets of evolution despite differences between organism's genetic background and environment.