The first sounds sub-standard. In the third, the adjective following a link verb is correct. In the fourth, 'hard' is an adverb.
That leaves only the third. This is the sort of snappy suggestion in which a breach of the rules of grammar is forgiven because of the crisp effect. There is also the point that 'eat healthily' somehow sems to suggests that there is some healthy way of chewing and swallowing, which is not what 'eat healthy' means.