The answer is the first option: a serpent whose poisonous body had covered an entire hillside and had required a thousand arrows to kill it.
For a structure to present parallelism, it has to repeat a certain grammatical form inside the sentence. Option a is the only option that presents such repetition. It is talking about the serpent's poisonous body and the two grammatical structures that come after that have the same structure: Past Perfect Tense.
It is as if two sentences were combined into one to avoid repetition:
A serpent whose poisonous body had covered an entire hillside.
+
A serpent whose poisonous body had required a thousand arrows to kill it.
=
A serpent whose poisonous body had covered an entire hillside and had required a thousand arrows to kill it.
Note: The third option (or option c) is incorrect because it says "requiring", not "required".