Miànduì duōduōbīrén de duìshǒu, tā bǎochí le lěngjìng.
Facing an aggressive opponent, she remained calm.
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咄 is an exclamation of reproach (like 'tsk!'). Doubled 咄咄 intensifies it. Combined with 逼人 (pressing on people), it paints a picture of someone aggressively confronting others with sharp words.