Before entering the level, backtrack to 2-2 to get drill.
In the first room, use drill to get running speed as you enter the level, but keep in mind that you can get stuck on the entrance. Drill is useful for clearing out the many enemies in the beginning of the room. The first instance is using the drill on the first set of Boneheads. Depending on when you started the drill at the very beginning, it's possible to clear all four of them before letting go of the drill, but since it travels faster than you once you let go, you might as well do it as early as possible. The second drill comes after the Galbo, right before the block. If you do it too early, the second Bonehead might not get hit.
Also in this section is a rare exception to the slope mechanic. Since they appear to be flowing hills of sand, it's faster to run down these small slopes instead of jumping over them. Once you reach the big skeleton, use the drill to break the stone block, get rid of your powerup, and grab Shard 1. After dropping into the hole, take the path to the left. In the miniboss strat shown here, the third fire attack skims the bottom of the Fishbone so that the fourth fire (which is shorter and also slowed down by holding right) lands you right on the exit. Four "direct" hits is probably less than a second slower. After the fight, grab Shard 2 on the left.
The next two rooms are just tests of single fire, but there are some small optimizations at the exits. In the first of these two rooms, it's possible to slide from flat ground onto the slope, causing you to get into the loading zone faster than just sinking in the water. For the other room, try to spend as little time in the water, but don't go too far to the right or else you'll waste time sinking in the water.
The water sections can be sped up a little bit with a few fires. For Shard 3 you can duck in the crevice with the Fishbone. You can also swim to the right of the skeleton piece that drops, but it's slower. Notice that while swimming up to it, Kirby doesn't need to slow down, even when the Fishbone attacks. After grabbing the shard, you can fit in three fires before reaching the exit.