The correct option is
B had taken
In order to fill in the blank with the correct form of the verb, we must understand the tense of the sentence.In the given sentence, the word 'managed' explains to us that the second half of the sentence is in the simple past tense. As there are two clauses in the sentence, and the second clause is in simple past tense, the first clause is bound to be in past perfect tense. There are two actions in the given sentence, the first clause is the action that happened before the action in the second clause. Hence, we will use past perfect tense for the first half of the sentence.
Option A - 'Took' is the past form of the verb 'take'. 'Took' is used in simple past tense. If we use both the verbs in simple past tense, then the sequence of the actions will be same. Hence, option A is incorrect.
Option C - 'Had been' is past perfect tense, but it means 'to be'. As the meaning doesn't match with the action in the sentence, we can't use 'had been'. Hence, option C is incorrect.
Option D - 'Taken' is the past participle form of the verb 'take'. As we need the helping verb 'had' with the past participle form of the verb to make past perfect tense, we can't use 'taken'. Hence, option D is incorrect.
Option B - 'Had taken' is the past perfect tense, and it indicates that the police had taken every precaution before she managed to rob the bank. Different tenses in a sentence show us the sequence of actions. Hence, option B is the correct answer.
'Although the police had taken every precaution, she managed to rob the bank.'