The correct option is C ill
The sentence is about a person "he" who speaks in a certain manner of his colleagues. This 'manner' is described by an adverb. Adverbs are words that modify adjectives, verbs and other adverbs to describe its manner, or the extent of something. We know an adverb is required here, because the word 'speaks' is a verb which can be only modified by an adverb. From the given options, 'ill' is the most suitable word, it means 'in an unfriendly manner'. Hence option C is correct. 'Illest' does not exist in Standard English, hence it isn't considered and option A is incorrect. 'Sick' and 'bad' are both adjectives, where 'sick' means 'afflicted with disease' and 'bad' means 'not good' or 'an evil character'. Adjectives don't modify verbs, nor are both these words relevant to the statement, unless they're in the adverb form 'sickly' or 'badly'. Hence options B and D are incorrect.