Negative campaigning is a central feature of political competition, yet empirical research has been limited by the high cost and limited scalability of existing classification methods. This study makes two key contributions. First, it introduces zero-shot Large Language Models (LLMs) as a novel approach for cross-lingual classification of negative campaigning. Using benchmark datasets in ten languages, we demonstrate that LLMs achieve performance on par with native-speaking human coders and outperform conventional supervised machine learning approaches. Second, we leverage this novel method to conduct the largest cross-national study of negative campaigning to date, analyzing 18 million tweets posted by parliamentarians in 19 European countries between 2017 and 2022. The results reveal consistent cross-national patterns: governing parties are less likely to use negative messaging, while ideologically extreme and populist parties -- particularly those on the radical right -- engage in significantly higher levels of negativity. These findings advance our understanding of how party-level characteristics shape strategic communication in multiparty systems. More broadly, the study demonstrates the potential of LLMs to enable scalable, transparent, and replicable research in political communication across linguistic and cultural contexts.