Perhaps the most interesting powerless section of the game. The main technique is described in the first clip: sliding and inhaling. The second clip shows the next segment, where you have to start dodging the Pupa enemies. In the same clip, there is the lone exception to sliding and inhaling. Since the platform after it is too high up, it is necessary to puff here instead of inhale. It is possible to slide off the platform in between the two Pupa, as shown on the right, but the positioning is pretty precise.
The first two clips show strats for dodging the Kapar enemies. The Kapars can be manipulated into jumping or not jumping based on your height when you come within a certain distance from them. I think that for the first section, both strats are of comparable difficulty and speed, but for the second section, the middle clip's strat is significantly easier, though with one fewer slide. Afterwards, you can find Shard 1 in a collapsible pit underneath a Pupa (right). I've managed to reproduce the TAS clip through the fake ground, but I don't know why it happens.
In the second room, Shard 2 can be found below the entrance. Since the drop is large, tap B to inhale momentarily so you don't faceplant. As usual, jumping up the vines is faster. The strat shown on the left for swallowing the Galbo is easier than it looks, but keep in mind that the way you approach him from underneath will cause him to wake up. A safer strat is shown in the middle. I've found that the most consistent way to reach the door is to use fire off of the vines, as shown on the right. Floating up from the leafy platform is probably just as fast.
The two strats shown here are in my opinion the most consistent way of getting two early cycles on the vines. This can be scary, as the death plane is basically right at the bottom of the screen, so if you don't feel confident in your single fire abilities, just take the vines as intended. In the first set of vines, skip the third and fourth vines by using fire underneath, and in the second set, skip the first two. The reason for grabbing onto the third and fourth vines in the second set is to take advantage of the large momentum boost you get from swinging on the vines. A crazy strat involves skipping the whole first set of vines and boosting off of two of the vines in the second set, but this is really precise and I haven't been able to execute it in a run.
The miniboss is straightforward: just hit it with fire. I like to do a small jump at the beginning so that I recover faster for the second fire. This is the same principle as the strat for the 1-1 miniboss. Afterwards, just walk into the loading zone instead of trying to slide. The loading zone slowly becomes unblocked, so if you slide at the wrong time, you'll bounce off of it.
This room has a lot of enemies, and since there's hardly any ground, losing your powerup is definitely a possibility. As in the room with the vines, the fastest strat is to get a boost off of the moving logs (left), saving about half a second over not doing it. If your single fire is consistent, a side benefit of choosing this strat is that the spacing is just right for the three pesky Pupa enemies right before Shard 3 (right). The Pterans are really annoying here, so make sure to avoid them carefully.
Grab the invincibility candy and blast through to the end of the room. I like to do three fires on the ground before jumping up. At the end of the level, make sure to grab the Cairn before exiting. Since it's a long stretch of single fire, your spacing might get messed up, so sometimes I like to just stop at the second to last platform and slide over to the Cairn.