It is well written, but not grammatically correct. Your first statement has no independent clause; it lacks a verb. A standard English sentence requires a subject and a verb.
It is a diary entry of a middle schooler in India as he remembers what happened during his summer holidays. He narrates the story that shook his life.
...as he remembers what happened during his summer holiday...a dependent clause
Writers sometimes use incomplete sentences when the idea can be understood without a verb, but it is the exception and not the rule.