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Question 1:

jugular (noun)
2: the most vital or vulnerable part of something <[He] showed an instinct for the jugular in competition>
[M-W's Col. Dic.]

Does it mean "He" would spare no weakness of his competitor in order to win?

Question 2:

Is the given sentence correct?

Does it mean "He" would spare no weakness of his competitor from his attack in order to win?

Please guide me. Thanks.
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Jackson6612Does it mean "He" would spare no weakness of his competitor in order to win?
Yes. Another useful phrase is "to go for the jugular".
Jackson6612Does it mean "He" would spare no weakness of his competitor from his attack in order to win?
Yes, but it is implied and, thus, no "from his attack" needed.
Comments  
Thank you, Fandorin.