The fastest way to switch from patient to hasty is by hitting the second help box in this level. It is slightly faster (about 0.2s) than switching on the world map. Do this by spitting an enemy into the help box. This is only faster on the Japanese version on the game, however, as there is one less text scroll. Spitting an enemy into the text box is slightly faster than jumping into it because you have to either collect a red coin or slow down a bit to jump into the box.
The hardest part of this level is the falling pollen section. There are many ways to navigate it safely, either by stopping and avoiding the falling pollen, spitting enemies at it, or using eggs. This video uses an egg route.
In a full-game run, you want to avoid collecting any red coins in order to save time at the score tally screen (it is minor, though: it saves half a second to have zero coins). After the falling pollen, do a double-tap jump off the middle post to avoid the red coins without having to flutter.
Getting between the chomp rock and the spore guy at 0:23 can be difficult. If your movement is slow at all you will get hit. It's only slightly slower to tongue the spore guy if you find that easier.
1-3 is otherwise very straightforward. It is recommended to exit the level with at least two eggs that can be used for 1-4.