The key to this question is the semicolon between the two blanks. It is a straight-ahead road sign that indicates the two parts of the sentence will support one another. We'll start with the easier blank, which is the second one in this case. We're told that Olivia's friends were astounded at how she handled dangerous situations. Because most people would be expected to avoid or fear dangerous situations, Olivia must be astounding in that she faces them head-on. We can make "accept" our prediction and check the answer choices. Choice (D) embrace, or "willingly accept," matches our prediction. Choice (E) undermine, which means "destroy" or "subvert," does not fit the context. Choice (F) shun, meaning "to keep away from," has the opposite meaning of the word we need.
For the first blank, remember that the semicolon is a straight-ahead road sign, so the first part of the sentence will support the meaning of the second. If Olivia faces danger head-on, a good prediction would be "fearless." Choice (B) dauntless means just that. Choice (A) feckless, meaning "ineffectual," does not make sense, nor does (C) guileless, meaning "honest."
The answers are (B) and (D).