That might have been the craziest party ever! which identifies the linking verb?

"have been" is the linking verb. If you can only choose one word, choose "been".

Explanation: Linking verbs connect the subject to the predicate (a predicate is a phrase that says something about a subject). So, here, the predicate would be "the craziest party ever", because it's referring to "that" in the sentence. The linking verb phrase, "have been", connects the subject "that" to the predicate noun, i.e. "the craziest party ever". Different forms of the infinitive verb "to be" are linking verbs, which also helps to determine the answer here, since "have been" is the past perfect tense of "to be".

My source, an excerpt from Merriam Webster:

Definition of linking verb

: a word or expression (such as a form of be, become, feel, or seem) that links a subject with its predicate

Examples of linking verb in a Sentence:

//“Look” in “you look happy” and “are” in “my favorite fruits are apples and oranges” are linking verbs.