Why is there such in interest in antibiotics against Pseudomonas?
Indeed Pseudomonas is a very peculiar (and concerning) genus in clinical microbiology, specially P. aeruginosa. The reason why you keep finding emphasis on antibiotics that have pseudomonal activity is because this organism is the model of bacterial antibiotic resistance. It is often considered more deathly than other important multi-resistant bacteria such as S. aureus, Acinetobacter or Enterobacter.

P. aeruginosa is responsible for multi-resistant nosocomial diseases (a basic definition of nosocomial is an infection acquired inside a hospital) that have really high mortality rates. It is not uncommon to see hospital antibiogram results for this bacteria informing about resistance for all the commmonly used classes of antibiotics for Pseudomonas infections including 3rd and 4th generation cephalosporins, fluoroquinolones and carbapenems.

Reference: Evolution of Pseudomonas aeruginosa Antimicrobial Resistance and Fitness under Low and High Mutation Rates

There are LOADS of articles and info to read about P. aeruginosa antibiotic resistance, but I like this one since it tries to explain how the problem appeared from a genomic point of view.