Navigating the first screen without unnecessarily slowing down can be tricky, especially because you want as many eggs as possible for 1-8. Other than that, Fuzzies are randomly generated, so you either need to clear the path in front of you by shooting an egg or two, by spitting one of the rolling enemies into the Fuzzies, or by just praying for good spawns. If you do get Fuzzied, jumping as soon as possible after touching the ground decreases the slowdown.
Be prepared for this if you decide to spit a Melon Bug (rolling enemy) into the Piranha Plant. Occasionally, the Melon Bug will clip right through the Piranha Plant without actually damaging it.
At the end of the fuzzy section, there is a pesky 1-up Shy-Guy who flies down right in your way. He can be cleared with a well-timed up-tongue.