This is actually a lot easier than it looks. I would suggest deliever papers to the first five houses and then race through the rest of the level to save a lot of time. Also you DO NOT need to finish the bonus level, I remember vividly trying to rush through the bonus part and screwing up and thinking I failed and the achivement popped, so you can simply crash as soon as you start the bonus course and it'll still be valid.
You can actually die at least once during the level and still earn the achievement. So just deliver five papers (count as you go along) and rush throught the rest of the level and you should get it.