Antimicrobial resistance (AMR) in Acinetobacter baumannii represents a critical global health challenge, particularly in intensive care settings where the pathogen causes severe, refractory infections. As a leading member of the ESKAPE group, A. baumannii has accumulated extensive resistance to multiple antibiotic classes, including carbapenems, resulting in the widespread emergence of multidrug-resistant (MDR), extensively drug-resistant (XDR), and pan-drug-resistant (PDR) strains. This review provides a chronological overview of the evolution of antimicrobial therapies used against A. baumannii, spanning the early era of penicillins and tetracyclines to contemporary agents such as eravacycline and ceftazidime–avibactam. We delineate the molecular mechanisms underlying resistance development, including carbapenemase production, robust RND efflux systems, horizontal gene transfer, biofilm formation, and the global dissemination of high-risk international clones (IC1–IC9). The compounding impact of the COVID-19 pandemic on the spread of carbapenem-resistant A. baumannii (CRAB) is also examined. A special emphasis is placed on Zosurabalpin, a first-in-class macrocyclic peptide antibiotic with a unique mechanism of action that targets the LptB2FG complex essential for lipooligosaccharide (LOS) transport and outer membrane assembly. Preclinical data and emerging clinical findings highlight its potent activity against highly resistant CRAB strains and its ability to circumvent conventional resistance pathways, marking it as a promising candidate in the antimicrobial pipeline. Finally, we evaluate the limitations of current treatment modalities and explore emerging strategies, including phage therapy, novel target discovery, and non-traditional therapeutics, offering a forward-looking perspective on restoring and sustaining effective anti-Acinetobacter interventions.