Turtle detective is not a turtle that wears a hat and uses a magnifying glass to solve crimes, it's a turtle that drinks a lot of alcohol and uses vulgar words in attempt to solve crimes.
Turtle has many names: Turtle, Snapper, Tramp, Drunk, Piss-ant, etc.
Turtle is not a hero. He is not a sidekick or a narrator. He is not even a "work in progress". Turtle is an idiot. His incompetence usually solves the case.
The turtle detective was born and raised a simple animal in the village of Rooftops.
He was not, however, content to live a mediocre life. He wanted more for himself and so, one day, he decided to leave his home.
He set off on his travels in search of more fortune and fortune he got, or at least he thought he would. He soon found that he was not the only one in the city looking for fortune and he quickly found himself in the middle of a turf war.
He didn't really want to be there. He wanted to leave, but for some reason he couldn't make himself leave.
The war continued onward and the casualties were starting to mount up. Soon, it became clear that one side would win, and one would lose.
This situation was like something out of a fairy tale, and the turtle felt he was ready to become a hero. It would not be hard, for in fairy tales, heroes always kill the monster and save the girl.
He remembered his story, of how he left his home because he was unhappy with life there. The turtle decided that the only way he could prevent himself from getting killed in this war was to become a "hero", and fight the monster that was about to destroy his village. What other choice did he have?
The turtle (who still wanted to be called "olaf", but had come to think of himself as a "hero" for some reason) waited until the very end of the fight.
Then, he did what any self-respecting hero would do : He jumped into the fray. And what happened? He punched out the leader of the other side and secured a big win for his side. He felt a rush of adrenaline, but that was soon replaced by exhaustion and the realisation that he had just fought a great battle. That night, he slept like a rock.
The next day, he returned to his village a hero. Well, sort of. The animals all respected him and he was extolled as a great protector of the humans, along with some preaching about how he should have fought the bad guy longer because the end result would have been the same anyway. He felt a certain pride at this, but he wanted more. He wanted to be celebrated for his actions, not just extolled. He wanted to be made out to be a real hero.
And so, he left again on his journeys, travelling to many different places in his search of a real adventure. This is where he became the Turtle Detective. He used his skills to fight monsters, solve crimes and generally be a real detective for hire. He did well for himself and he even acquired a sidekick in the form of an intelligent rat.
And that is how olaf became the Turtle Detective, trying to find real justice in a world of make believe.