Antimicrobial polymers represent a novel class of antimicrobials to tackle AMR. Their primary mechanism of action of membrane disruption may allow them to bypass conventional mechanisms of resistance and reduce the likelihood of resistance evolution. Despite this, the processes driving resistance to these compounds remain poorly understood. In this work we have evaluated a library of block copolymers, with the copolymer referred to as aT50, being the standout compound in this current library. This copolymer demonstrated activity against P. aeruginosa with MICs of 16-32µg/mL, with limited in vivo toxicity in a Galleria mellonella model. Furthermore, the copolymers synergise with the clinically relevant anti-Pseudomonal antibiotic polymyxin B in both planktonic culture and high-validity models of biofilm infection. This interaction was shown to occur through enhanced membrane disruption and disruption of the biofilm structure. To explore resistance evolution to this promising compound, we selected for resistance in six populations of PA14, isolating clones from early and late timepoints in an evolutionary ramp experiment. Phenotypic analysis identified that only low levels of resistance emerged (average 2-fold increase in MIC), which was associated with a decline in fitness in the absence of the copolymer and loss of virulence, with increased survival in a G. mellonella infection model. Genome sequencing revealed a high frequency of SNPs in PhoQ and PmrB- genes associated with resistance to charged agents- yet cross resistance to such antimicrobials remained minimal. Overall, these findings support the use of the copolymer aT50 as a promising therapeutic candidate for tackling Pseudomonas aeruginosa infections.