Here's the most seamless way to get from the first world to the eighth (final) world of the game.

1.) Play until you get to Level 1-3. Here, you should dash to the end of the level until you get to a white platform near the end. Stand atop it, hold down until you "fall behind it", and run to the end of the level. You'll acquire a Warp Whistle.

2.) Play from there until you reach the World One Fortress. Make sure you're Raccoon Mario as you traverse the stage (ignoring the Fire Flower you are offered). At the end, you can go through a door, or you can fly high above and over the door. When you do, run to the right (you won't see your character) and press Up to enter a secret room. Within is another Warp Whistle.

3.) Now, select one of the Warp Whistles from your menu and use it. But don't select a destination world! Instead, use a Warp Whistle, your second, right after you use the first. This will allow you to access the eighth and final world of the game.