Antimicrobial peptides (AMPs) contain amphipathic structures and are derived from natural resources. AMPs have been found to be effective in treating the infections caused by antibiotic-resistant bacteria (ARB), and thus, are potential lead compounds against ARB. AMPs’ physicochemical properties, such as cationic nature, amphiphilicity, and their size, will provide the opportunity to interact with membrane bilayers leading to damage and death of microorganisms. Herein, AMP analogs of [R4W4] were designed and synthesized by changing the hydrophobicity and cationic nature of the lead compound with other amino acids to provide insights into a structure-activity relationship against selected model Gram-negative and Gram-positive pathogens. Clinical resistant strains of methicillin-resistant Staphylococcus aureus (MRSA) and Escherichia coli (E. coli) were used in the studies. Our results provided information about the structural requirements for optimal activity of the [R4W4] template. When tryptophan was replaced with other hydrophobic amino acids, such as phenylalanine, tyrosine, alanine, leucine, and isoleucine, the antibacterial activities were significantly reduced with MIC values of >128 µg/mL. Furthermore, a change in stereochemistry caused by d-arginine, and use of N-methyltryptophan, resulted in a two-fold reduction of antibacterial activity. It was found that the presence of tryptophan is critical for antibacterial activity, and could not be substituted with other hydrophobic residues. The study also confirmed that cyclic peptides generally showed higher antibacterial activities when compared with the corresponding linear counterparts. Furthermore, by changing tryptophan numbers in the compound while maintaining a constant number of arginine, we determined the optimal number of tryptophan residues to be four, as shown when the number of tryptophan residues increased, a decrease in activity was observed.