You should try the second option ( hyperbole)
This is an 'adverb infinitive'. It is not a participle, either present of past, because it doesn't end in -ing. And it is not an 'adjective infinitive' since its meaning is adverbial, 'you must capture or trap the other king' IN ORDER 'to win a game of chess'. Adjective has to modify a noun, which isn't the case in this sentence.
C. is you are referring to the coach
Answer:
He has no intention of truly alleviating Hester’s suffering.