The preparation of a soybean flour adhesive with good bonding and prepressing performance, toughness, mildew resistance, and fire retardancy to address the problem of formaldehyde pollution is crucial; however, it also presents a challenge. The core–shell structure can achieve various properties by tailoring-making the core–shell composition. In this study, a core–shell structure HBPA@TA with hyperbranched polyamide (HBPA) as the core and tannin (TA) as the shell was prepared and used to modify SF adhesives. The results showed that the pyrogallol group of the tannin shell endowed the adhesive with excellent prepressing performance (0.75 MPa of prepressing intension), toughness, and coating performance, rendering the adhesive more suitable for plywood fabrication. Owing to the dense tannins in HBPA@TA, the resultant adhesive exhibited superior mildew resistance (12 d). After closed-mouth placement for 12 d, the prepressing intension was reduced by 17.3% to 0.62 MPa, which still met the usage requirement. The wet shear strength of the plywood prepared using the resultant adhesive was 1.05 MPa—that is, 133.3% higher than that of the unmodified SF adhesive. The synthesized adhesive also showed antibacterial properties (inhibition zone = 8 mm), flame retardancy (LOI = 32.3%), and volatile organic compound release (6.86*106 mg/m2·h) lower than those of commonly used urea–formaldehyde resins and epoxy resins.