Eat yourself / Eat yourself adj [closed]
In this case, the sentence is shorthand for this form:
Eat [a certain, unspecified way] to become [something].
Whatever that something is, it is an adjective in this case. By comparison, it's an adverb here:
Eat [somehow].
So, substituting "smart" in:
Eat yourself smart.
Eat smart.
What do you become after the first sentence? You become smart. How do you do that? It's unspecified.
What do you become after the second sentence? It's unspecified. How do you do that? By eating in a smart way.