<p>We study the large-order asymptotics for the Kuznetsov–Ma breathers of the nonlinear Schrödinger equation in the far-field regime. Utilizing the Darboux transformation, we first derive the corresponding Riemann–Hilbert representation for the high-order Kuznetsov–Ma breathers. Under the far-field limit, we identify that there are four asymptotic regions in the space–time plane where the breathers exhibit different behaviors: a genus-two region, an algebraic-decay region, a genus-zero region and a non-oscillatory region. By applying the Deift–Zhou nonlinear steepest-descent method, we provide the leading-order term for each region and numerically verify the consistency between the exact solution and the asymptotic solution. In contrast to previous studies on the large-order asymptotic analysis of rogue waves and solitons, we discover a novel genus-two asymptotic region, which enriches the understanding of large-order dynamics.</p>