In the given sentence, the difficulty of the lesson is being compared to the subject's expectations. In order to make this comparison, the answer must be an adjective of the comparative degree.
Option A is correct. 'much harder' is an adjective of the comparative degree. It indicates that the lesson was more difficult than what the subject had expected. Thus, it is correct.
Option B is incorrect. 'the hardest' is an adjective in the superlative degree. Thus, it cannot be used to make a comparison.
Option C is incorrect. In 'most hard', the word 'most' indicates superlative degree but, 'hard' is in positive degree. Thus, the phrase itself is incorrect.
Option D is incorrect.In 'more hard', the word 'more' indicates comparative. degree but, 'hard' is in positive degree. Thus, the phrase itself is incorrect.