We consider the Cauchy problem for the focusing nonlinear Schrödinger equation with initial data approaching different plane waves Ajeiϕje-2iBjx, j= 1 , 2 as x→ ± ∞. The goal is to determine the long-time asymptotics of the solution, according to the value of ξ= x/ t. The general situation is analyzed in a recent paper where we develop the Riemann–Hilbert approach and detect different asymptotic scenarios, depending on the relationships between the parameters A1, A2, B1, and B2. In particular, in the shock case B1< B2, some scenarios include genus 3 sectors, i.e., ranges of values of ξ where the leading term of the asymptotics is given in terms of hyperelliptic functions attached to a Riemann surface M(ξ) of genus three. The present paper is devoted to the complete asymptotic analysis in such a sector.