It is extremely difficult to train a superhuman Artificial Intelligence (AI) for games of similar size to StarCraft II. AlphaStar is the first AI that beat human professionals in the full game of StarCraft II, using a league training framework that is inspired by a game-theoretic approach. In this paper, we improve AlphaStar's league training in two significant aspects. We train goal-conditioned exploiters, whose abilities of spotting weaknesses in the main agent and the entire league are greatly improved compared to the unconditioned exploiters in AlphaStar. In addition, we endow the agents in the league with the new ability of opponent modeling, which makes the agent more responsive to the opponent's real-time strategy. Based on these improvements, we train a better and superhuman AI with orders of magnitude less resources than AlphaStar (see Table 1 for a full comparison). Considering the iconic role of StarCraft II in game AI research, we believe our method and results on StarCraft II provide valuable design principles on how one would utilize the general league training framework for obtaining a least-exploitable strategy in various, large-scale, real-world games.