Why is (是) shi4 dropped in this sentence："我很好"?
Simply put, adjectives in Chinese can function as verbs.

More specifically, they can form predicates without the use of a copula verb such as 是. For this reason, adjectives in Chinese are sometimes considered to be a class of verbs called "stative verbs".

You can refer to the answers of this previous question for more details: Stative verbs in Chinese: only for adjectives?