I'll pick up where DanHibiki left off.

The boss he speaks of is quite tough. Whenever you shoot it, it shoots little fireballs from its head, not unlike a volcano. The key to defeating it is to get a running start and try to jump over its head. When you are above its head and look like you're going to kick it, hit jump again and the jet blast will hit it in the head. This does a lot more damage than a shot from your hands. The point here is to hit the boss with a jet blast, which then sends you flying away from the fireballs. This move also keeps the boss from blocking you into a corner.

The next level is another rather annoying boss battle: you are a cricket, on a mat. The mat unrolls at the top of the screen and rolls back up at the bottom. There are obstacles on the mat that you must run past. You also have to shoot the gigantic hands that attempt to crush you. On this level, you really have to hit the hands hard, while trying to keep from falling off the mat. If you simply concentrate on staying on the mat, the extremely short time limit will kill you, or you'll get crushed by the hands. This is a surprisingly difficult level.

The exact progression of levels after that slips my mind.
While none too original, this is actually among the better platform games out there, if only because it's very well-executed. There are no obvious flaws in the game, and no ingratiating oversights. One thing to note is that you have to move to shoot diagonally up, but this isn't much of an issue.

Here's a tip that can help on any difficulty level. There is an enemy that appears in almost every level called the "Beedle." It looks like a fly and usually appears in groups of three to five. Of all the enemies in the game, Beedles are the easiest to kill, and they regenerate. Therefore, you can simply go to a "respawn point" and wait for more Beedles to appear, and kill them until they drop health or a multiplier.
(Remember that multipliers affect 1-ups - if you have a 3x multiplier, the 1-up will give you 3 lives! If you find a 1-up, go back and kill Beedles until you get a multiplier, then grab the 1-up.)