means "undeterred by", "making nothing of": someone faces a hardship and carries on as if it were nothing. It goes straight after a noun naming the hardship – an injury, bad weather, criticism, danger.
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He played in the match, undeterred by his injury.
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She kept chasing her dream in spite of everyone around her objecting.
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They kept climbing, undaunted by the strong wind.
The sentence praises someone else's courage, so it is not used about yourself, and the noun is always something hard to bear. The form with means the same. It belongs to writing: news, biographies, speeches. In conversation, にも負けずに says much the same: .
をものともせず or をよそに
also means "paying no attention to", but what is ignored is other people's worry or opinion, and the speaker usually disapproves.
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The firefighters charged into the burning building, making nothing of the danger.
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Ignoring his parents' worries, he set off abroad alone.
Lingaku