Sustainability reports are key for evaluating companies' environmental, social and governance, ESG performance, but their content is increasingly obscured by greenwashing - sustainability claims that are misleading, exaggerated, and fabricated. Yet, existing NLP approaches for ESG analysis lack robustness against greenwashing risks, often extracting insights that reflect misleading or exaggerated sustainability claims rather than objective ESG performance. To bridge this gap, we introduce A3CG - Aspect-Action Analysis with Cross-Category Generalization, as a novel dataset to improve the robustness of ESG analysis amid the prevalence of greenwashing. By explicitly linking sustainability aspects with their associated actions, A3CG facilitates a more fine-grained and transparent evaluation of sustainability claims, ensuring that insights are grounded in verifiable actions rather than vague or misleading rhetoric. Additionally, A3CG emphasizes cross-category generalization. This ensures robust model performance in aspect-action analysis even when companies change their reports to selectively favor certain sustainability areas. Through experiments on A3CG, we analyze state-of-the-art supervised models and LLMs, uncovering their limitations and outlining key directions for future research.