It's not that hard at all, but you'll need a firm grasp of how the games works. I strongly suggest you to try this after your first successful run.
It's much, much, muuuuuuch easier to try this on the fourth area on easy (normal) mode. You can't land anywhere, you can't go to a bonus area or a shop, keep that in mind. When you enter a new sublevel, go directly to the right or the left to avoid the starting platform. Go slowly, shoot intermittently, it will go well. You can land on every bits on pieces on your way, the're here so you can refill and keep your combo up. Be methodical, shoot everything on your way, rinse and repeat, don't forget to avoid the starting area and the shops/bonus rooms on 4-2 and 4-3, and voila.
It will be a little bit easier if you have the jetpack upgrade. With it, when you're out of bullet, you'll go a bit slower if you keep pressing your shoot key. Not necessary, but it will help.