Large Language Models (LLMs) remain vulnerable to jailbreak attacks despite extensive safety alignment. While automated red-teaming has emerged as a critical evaluation protocol, existing methods face two primary limitations: they largely explore homogeneous transformations in isolation, and they rely on brittle judgment metrics that frequently misclassify non-refusal hallucinations as successful attacks. In this paper, we reformulate jailbreak attacks as a compositional search problem guided by context-aware evaluation. We propose Chimera, a framework that generates compositional jailbreak attacks via judgment-driven search over heterogeneous strategies. Chimera systematically explores the combinatorial space of disjoint primitives, such as integrating technical obfuscation with semantic persuasion, under strict ordering constraints. Crucially, to drive the search process effectively, we introduce StrongREJECT++, a relevance-aware metric that eliminates false positive rewards by penalizing irrelevant responses. Experiments on multiple open-source and commercial LLMs show that Chimera uncovers qualitatively different vulnerability regions and consistently improves attack success rates and transferability compared to state-of-the-art baselines.