This paper investigates the formation maneuvering control problem for multi-agent systems with limited sensing capabilities, proposing a novel control framework based on prescribed-time control theory. By constructing time-varying performance functions to constrain distance errors, the system achieves precise convergence within a user-prescribed time while guaranteeing transient performance, collision avoidance and connectivity maintenance. Unlike existing asymptotic or finite-time control approaches, the proposed scheme incorporates time-varying gain mechanisms and a universal barrier Lyapunov function to drive distance errors into an arbitrarily small neighborhood of zero.