In the beginning of the level, combine for drill and avoid enemies along the way to the needle barrier. The best way of taking care of these Rockies is to headbutt them, but for the one next to the barrier, you can use a kind of damage boost off of one of them while using drill. When using the drill horizontally, normally it won't hit something below it, except in situations like this where the tip of the drill is above the side of the barrier. While using the drill, the Rocky will fall on you and cancel the drill animation, allowing you to start falling faster to obtain Shard 1. Since there's a maxim tomato towards the end of the previous level, there should be no risk, but shooting the drill downward is an alternative.
The Bouncys are kind of annoying in how they're spaced apart. A simple strat is to just drill through them (bottom-left), but you can avoid that by some careful movement (bottom-right). At the end, hold the Propeller enemy in your mouth.
Combine for curling stone on the Cairn. Fluent curling stone movement boils down to following a route. While I'm not going to show my whole route here (and besides, everyone's route is different), I decided to show what I thought were the crucial parts. When you're just starting out, it's probably not a good idea to use curling stone unless you're doing it over a long and flat region. As seen in the middle, narrow spaces with enemies are usually too risky to use curling stone on. Later on in the same room, there will be four thin columns. It's possible to squeeze in a precise curling stone in this region.
The Adeleine painting has three possible patterns: parasol (top), pizza (bottom-left), and top hat (bottom-right). The parasol one is kind of tricky because you need to break three blocks in the top row, and Kirby's puff can only reach two blocks from one spot. For top hat, you complete the block puzzle far away from Shard 2, but luckily it can be reached fairly easily using curling stone. One optimization that can be done for all three patterns, but is especially useful for top hat, is puffing two blocks in succession by positioning yourself in between the heights of the two blocks.
After the puzzle is an easier curling stone section. As shown in the top-left, I like to jump starting from the space just left of the Cairn to make the subsequent platforms easier. It's really easy to headbutt the Fishbone's head and fall to your death, so wait a little bit while it passes over you before jumping into a curling stone. Once you reach some collapsing platforms, start floating up after jumping off the second one and land on the highest block (top-right). After this flat area, drop down for Shard 3 and float back up. The ending doesn't really have a nice route for curling stone (bottom-right), so you'll have to float a bit.