To automatically tune configurations for the best possible system performance (e.g., runtime or throughput), much work has been focused on designing intelligent heuristics in a tuner. However, existing tuner designs have mostly ignored the presence of complex performance requirements (e.g., the latency shall ideally be 2 seconds), but simply assume that better performance is always more preferred. This would not only waste valuable information in a requirement but might also consume extensive resources to tune for a goal with little gain. Yet, prior studies have shown that simply incorporating the requirement as a tuning objective is problematic since the requirement might be too strict, harming convergence; or its highly diverse satisfactions might lead to premature convergence. In this paper, we propose CoTune, a tool that takes the information of a given target performance requirement into account through co-evolution. CoTune is unique in the sense that it creates an auxiliary performance requirement to be co-evolved with the configurations, which assists the target performance requirement when it becomes ineffective or even misleading, hence allowing the tuning to be guided by the requirement while being robust to its harm. Experiment results on 162 cases (nine systems and 18 requirements) reveal that CoTune considerably outperforms existing tuners, ranking as the best for 90% cases (against the 0%--35% for other tuners) with up to 2.9x overall improvements, while doing so under a much better efficiency.