The correct answer is (B).
Keep in mind that this sentence has two parts: a dependent clause beginning with the word "despite" and an independent clause, which begins after the comma. To help you figure out the answer, you need to decide how these clauses are related. There is a clue in the first part of the sentence, the word "despite," indicating that there is a contrast between the clauses. The second clause also has important information because we know she has earned "a reputation as a backstabber." Therefore, the second blank will be related to "backstabber." The clue for the first blank lies in the phrase "harmless facade," which means she was very good at seeming innocent -- the definition of the word we need for the first blank.
Choice (B) is our answer since we are looking for something that means "deceit" for the first blank ("chicanery" means just that) and a word that is defined as "hostile or unfriendly" ("inimical") for the second blank. Be wary of choice (A) because "respected" will not suit the last blank -- this cannot be our answer. "Agreeableness" in choice (C) is also tempting if you have skimmed the sentence, but "sublime" means "noble" and makes this choice incorrect. Choice (D) is also wrong because "latency" or "inactivity" does not fit the sentence, although "antagonistic" does fit in the second blank. Choice (E) is not suitable, even though "equivocation" ("duplicity") could work in the first blank, because "dilatory" ("tardy") is not related to hostility or unfriendliness.
