Official Explanation
Split #1: hold that vs. hold to be. The correct idiom with the verb "hold" is a "that"-clause --- hold that P is Q. Choices (A) & (B) have this correct structure. The structure "hold P to be Q", using the verb "hold" with an infinitive phrase, is incorrect. Choices (C) & (D) & (E) make this mistake.
Split #2: parallelism. The main clause is "Ancient Celtic legend holds" --- the direct object of the verb "hold" is a "that" clause, which takes up the rest of the sentence. Within this that clause, the subject is "the mythical figure of Arthur" and the two verbs of this subject should be in parallel. These two verbs are "was" and "will arise", which only Choice (A) has. The "was arising" in choice (B) is not parallel. Notice, the two verbs are not in the same tense, but this is fine: verbs in parallel need not have the same tense.
The only possible answer is choice (A).