Is it grammatically correct? I'm not sure because smoking is verb and academic achievement is a noun. If it's not what is the correct sentence?
I would choose "relationship between smoking and academic achievement."
Smoking is a gerund here, an -ing verb acting as a noun to describe the act of doing something, so comparing it to "academic achievement" is appropriate. As mentioned by tunny, this is a sentence fragment as it stands, not a complete sentence.
"The relationship between smoking and academic achievement is..."