In the given sentence, 'than' indicates that the subject and the object is being compared to each other. The comparison is made between a mutual quality of both. Thus, the answer must be an adjective of comparative degree.
Option A is incorrect. 'badly' is an adverb and not an adjective. Thus, it cannot be the answer.
Option B is incorrect. 'too badly' is an adverb and not an adjective. Thus, it cannot be the answer.
Option C is incorrect. 'worst' is an adjective of the superlative degree and not the comparative degree. Thus, it cannot be used for comparison.
Option D is correct. 'worse' is an adjective of the comparative degree and thus, it can be used for comparison. Thus, it is correct.