Personal narrative. This is like a life story as it is a story told from an individual's point of view. It includes all the important aspects of one's life, such as the challenges faced, the relationships, and the achievements. It is a way for a person to share their unique journey through life.
Life account. A life account can also be used to refer to a person's life story. It gives a description of the events, experiences, and development throughout one's life.
A story of love can also be called a love narrative. It emphasizes the aspect of it being a narrative that revolves around love. For example, many classic novels are love narratives where the plot is centered on the relationship between two characters in love.
Business achievement chronicle.
No, it's not a common phrase. I've rarely heard it in everyday language or common literature.