You cannot tell a story in the present perfect: the narrative needs to be in the past tense. The main events in your story should be in the past simple, with occasional uses of the past continuous and past perfect to give some context. For example, you'd use the past continuous to say what was happening around the time when the event took place e.g. "Jack was driving along a country road when the accident happened" or the past perfect to give context about the situation before the event took place e.g. "Jack had never driven in that part of the country before".
We don't tell stories in the present perfect. This is because the present perfect is not a past tense : its function is to tell us something about the present moment. The only time we can use the present perfect in a story is when we are relating the events of the story to the present time. We often do this just at the beginning or the end of the story.
For example, you might begin your story with a single instance of the present perfect by saying "The most frightening thing that has ever happened to me was when I spent a night in a haunted castle in Transylvania." You would then tell the actual story in the past tense - NOT the present perfect. Once you establish when something happened, you have to continue in the past tense. Then, at the very end, you might relate the story to the present again by saying "and I've never dared to go back" or "I've been terrified of bats ever since".