I'm crazy busy.

Literal

Busy-[emphatic-くって], crazy [copula-だ].

くって is an emphatic/colloquial variant of くて — the geminate っ adds emotional intensity, like stressing the word in English. クレージー is a katakana loanword from English 'crazy,' used here as a na-adjective predicate. The sentence is very casual and expressively exaggerated.