At the beginning of the level, headbutt (or jump over) enemies until you get fire (left). In the second room, float up instead of taking the Zebons, grabbing Shard 1 along the way (right). Though you can squeeze through the Scarfies, it's faster to stay left and fire over because the platform is lower.
Hold the Emp enemy in your mouth as you navigate to the right, combining with the Poppy Bros. at the end (left). There are few things to be careful about. If you're too close to the Emp, you can swallow the enemy behind it. The Gloms (frogs in the wall) will destroy anything in your mouth, so it is imperative that you jump quickly past them. A safer strat would just be to swallow and take out the powerup later. Finally, I like to spit the enemy out in between the two sets of collapsing platforms so that I don't lose running speed. For whatever reason, you go back to walking speed if you spit on those platforms, even before they fall down.
In the room afterwards (right), just jump and avoid enemies. The two floppers are in the way, so puff them out of the way. The waterfalls push you down, so account for that when jumping.
Drop below the miniboss and run into it with the snowman powerup. After the four hits, the platform will sink, revealing Shard 2. To get to the door when the Tick enemy on the right is still there, just float up and walk towards the exit. Depending on its movement, you might be able to just jump over it or freeze it incidentally during the actual fight, allowing you to reach the exit more directly.
Navigate towards the bottom of the room and break the block with the snowman powerup. When climbing down the platforms, I like to hug the left side, but some people prefer to go more towards the middle. Since the snowman attack lasts so long and there's nothing nearby to help you break the block, you should activate it as soon as possible (i.e. once you reach the lowest level) to minimize the waiting time. After getting shot up into Shard 3, remove the powerup while falling to avoid faceplanting and run it into the Zoos. To avoid the Kapars, just run over the blocks.