You can only do this in the epilogue (last chapter). It doesn't work in chapter 4 when you play the Crash Bandicoot game for the first time. The reason being that you have an extra life in the Epilogue which gives you 500 bonus points.
You must beat the highscore of 3500 points. With a few tries this is quite doable. You need to pick up most of the apples, don't die, and complete the game as quickly as you can. If you are short a few points it's because you didn't pick up enough apples or missed the bonus life from one of the boxes. The bonus life is found in a wooden box relatively early in the level. If you don't pick up the bonus life you cannot beat the highscore.