应接不染的英语表达方式为 "unflappable" 或 "cool under pressure".
"Unflappable" 源于 "flap" 这个词，意思是 "慌乱，焦躁"，所以 "unflappable" 就表示 "镇定，不慌不乱"。"Cool under pressure" 则是指在压力下保持镇静的状态。
下面是一些英文例句和中文翻译：
She's an unflappable leader who never panics, no matter how dire the situation. 她是一位冷静的领导人，无论局面有多么糟糕，她都不会慌乱。
He's a calm, unflappable person who never seems to get ruffled. 他是一个冷静、不慌不乱的人，似乎从来都不会慌乱。
She's known for being cool under pressure and able to handle any crisis that comes her way. 她以在压力下保持冷静著称，并能够应对任何危机。
He's a cool customer under pressure, and he always manages to stay focused and composed. 他在压力下是一个冷静的人，总是能够保持专注和镇静。