This paper addresses the vulnerability of large-scale language models (LLMs) to hardware-based threats, especially bit-flip attacks (BFAs). While previous studies have argued that transformer-based architectures are more robust against BFAs, this paper shows that even a few bit-flips can severely degrade the performance of LLMs. To this end, we propose AttentionBreaker, a novel framework that efficiently explores the parameter space of LLMs to identify important parameters. In addition, we present GenBFA, an evolutionary optimization strategy that finds the most important bits and improves the attack efficiency. Experimental results show that even a few bit-flips can drastically degrade the performance of LLMs. For example, in the LLaMA3-8B-Instruct model, the accuracy of MMLU tasks drops from 67.3% to 0%, and the perplexity of Wikitext jumps from 12.6 to 4.72 x 10^5 with just three bit-flips. This highlights the effectiveness of AttentionBreaker and the vulnerability of LLM architectures.