The nightmare level of many any% runs. Bounce on the fish at the start of the level to skip the platform/flame melon. Next, perform an extended flutter by bouncing on a jumping fish in the water (make sure to hold down jump prior to bouncing, or you won't go high enough). This allows you to run along the top of the level and safely skip part of the level.
The next area is just tight jumps over slippery surfaces. Skipping super baby mario is the fastest route.
In the next area, when bouncing on the snowmen, you must manually release jump and repress it to flutter: you cannot bounce on them and simply hold jump for an auto-flutter like most other enemies in the game.
There are many ways to increase the speed of the skiiing section by jumping at the right times to avoid upward slopes or flying too long in the air, but they can be quite risky. There is probably an optimal and safe route waiting to be discovered. Check the Japanese runs on nicovideo, or the any% TAS on tasvideos.org for ideas.