In the first room, run forward and jump into a double fire so that the recovery happens when you're over the pit. Follow the double fire route and drop down for Shard 1. Note that the first double fire in the second room should be as early as possible, so just mash when you first start the room. I suppose that instead of puffing, you could double-fire into the shard, but that's pretty risky because the camera angle there is bad. Shard 2 is located in the top-left of this Zebon room. Note that the Zebon is spinning clockwise and "rounds up": if you press A in between, e.g., west and northwest (right), it'll stop at northwest. This also means that it's not possible to immediately shoot upwards. Follow the double fire route until you reach the Ticks. Swallow one and continue onwards. For the set of blocks with the Mopoos and Cairns, you can use needle (middle) or jump on top (right), though the latter is more precise and depends on the Mopoos' cycles. In the room with the pink clouds, most enemies can be headbutted or simply jumped over, but the Maws require you to manipulate its jump height by running into the slope a little bit before jumping.

Towards the end of the room, combine for lightning rod with the Sparky. The Sparky can jump off into the pit, as shown in the bottom-left, so the best way of respawning it is to go to the right, kill the Maw, and walk back to the left. In my experience, using the needle at the peak of your jump right above the Maw is the most consistent way of hitting it. If the Sparky tries jumping off again, you can intercept it since you're now standing closer to the hole. As with the other Sparky combination in 2-1, missing the throw wastes a lot of time, so be very careful.

The end of the level has a Maw on the ceiling, which can be bypassed by jumping near it, and a set of four Mopoos. Since their cycles can be a bit strange sometimes, I like to jump preemptively for the ones that spawn from below. The miniboss is pretty random, but if you stand at the bottom below the barrier, you should be in a good position most of the time. Sometimes, the lightning rod can get off two hits because the Mopoo has few invincibility frames. After the fight, grab Shard 3 and slide out. The reason for keeping the powerup will be seen in 5-3.