You start above ground but you have no choice but to jump into the hole in front of you. You'll fall onto a platform below when you do. Now fall off the left side and fire at those Mines moving around. They will shoot out spikes when you hit them so either jump or duck under them. At the edge to the right, jump to the platform above but watch out for the Spark moving around it. It's best to just jump extra high so you'll float over it and land on the ground ahead. You can do this for this Spark as well but you'll have to be more careful because of the spikes above. Hit the Mines on the right and then make your way up to be above water again.
Head right and get into the Booster ahead to get sent flying. There's a Heart Container on a platform to the left but don't get out right away, wait until just after you see the ceiling. Now jump back into the Booster and go right before a little after that. You don't want to wait too long because there's some inertia when you get out of it. Keep doing this until you reach the last one. Now this time go reasonably high and press right when you fall out. The reason for this is that there's spikes along the floor. Once you're back on the ground, you'll have to drop into the water again. Jump over the spikes on the floor and kill any Fish that comes at you.
Fall into the hole and head right to avoid the spikes and then down the stairs. There are Electric Eels here. Kill them or avoid them but head down the next set of stairs. Directly to the right of the stairs are three Mines and they are very close to you. Do a short hop and hit the two lower ones if you can while their spikes are diagonal. That should help you avoid getting hit. At the far right there's another Spark moving around a platform. Jump to the platform and again to the next one. Kill any of the Subs that come toward you.
It's a good idea to continually use your Spread Fireballs so you can kill any of them at appear at awkward times. You'll want to do this for sure when you jump to the tiny platform ahead and then to the ground where the stairs are. You don't have to hit the first Mine but you'll have to destroy the second one to reach the stairs. Electric Eels will appear during the next two platforms along with a Mine floating near the stairs. Hit the Electric Eels that get in your way as well as the Mine while it's spikes are diagonal and then climb the stairs. You're in the clear from this point forward so climb the stairs to find the boss.
Boss: Bubble Octopus
The boss doesn't have an absolute attack pattern. It will float around in its bubble, trying to hit you. Switch to your Spread Fireballs use them to get in lots of hits. Standing backwards from the boss while using the Spread Fireballs is a good way to make your shots more accurate. Either that, or fire upwards when it's above you. Avoiding the boss is fairly simple. Just watch where it appears and move out of the way. Avoid jumping if you can and duck when he floats across the screen. When you hit him enough times, he'll float to the center of the screen and he and his bubble will dissolve.