As it is with snow and ice, you'll slide if you try to stop while you're running. Tap the directional pad in the opposite direction that you're moving to stop the slide. Run to the right and then across the four icebergs. After the fourth one there will be an Ice Guy standing on the far right. Hit him with a fireball to kill him but don't get too close or he will start tossing popsicles at you (yeah, you heard right, popsicles). These next four icebergs are tougher to cross, as they sink and rise out of the water repeatedly. The first two are all right, just jump to them. The third one is tricky since it's out of sync with the first two. You'll have to wait until the second one is nearly underwater and then jump to the third one.
The fourth one is simple to get to but keep an eye out for the Ice Guy standing slightly off screen. Hit it when you see it. Keep going and melt the Snowmen that you see waiting ahead. If you get too close, they will jump over you. It's not a problem though. A Heart Container will be waiting for you at the elevated ground ahead and along with another Ice Guy in the dip, followed by a Seal at the top of the hill. Continue to the right and jump into the hole in the ground. In the ice cave below there will be several moving platforms. Fall onto the first moving platform when it gets close, don't jump or you might hit the spikes overhead. Do the same thing when you see the next moving platform, and then jump onto the solid ground at the far end.
There will be a Frozen Duck to meet you ahead, followed by another one towards the next set of moving platforms. Hit them while they are still running at you, and jump over them if they go into a slide. When you reach the moving platforms ahead, you should just drop onto one of them, as well as the next one. Jump to grab the Heart lying on the ground and fall onto the next set of moving platforms as usual. When you reach the far right side, wait until the moving platform starts to turn downwards before you jump to the ground ahead. You don't want to die and start over when you've gotten this far do you? =). Fall onto the ice below and switch to your bat transformation special. Charge it up and fly across the spikes.
Now do the same thing here but be careful. Fly somewhat above the platform on the left and then fly diagonally into it to transform back. If you don't do this, you might transform back while you're at the edge and then you'll fall into the spikes hanging down. I'm weird and probably paranoid but it happened to me. This next one is tough. You have to keep a steady hand here or you'll fall to your death or run into the spikes that line this next area. Transform and carefully make your way up into the spike area. Fly across it and try to stay in the middle and not too close to the spikes. Once you reach the far end with the wall and the drop down, you can just hit the wall and transform back. You'll end up back on solid ground, or icy ground if you want to call it that.
Walk to the far right, switch to your Spread Fireballs and hit the Seal there. Do the same thing with each of the Seals ahead but don't get too close or it'll toss that bomb on its nose at you. And let me tell you that it's not a pretty sight being hit with it. At the top use your bat transformation again to get over that wall with the Full Heart on it. You're almost in the clear but there's still a little ways to go yet. You should see a Skater ahead. Kill it just as you see it or it'll jump at you and start skating around. There will be two more of them ahead. Get rid of them and you'll be out on the water. The boss is just ahead.
Boss: Mr. Dragon
This boss is so simple it's almost bordering on pathetic. Almost. It has a few tricks up its sleeve though. It starts off by flying around the screen randomly. Take this time to switch to your Spread Fireballs and start hitting it as much as possible. After awhile it'll start flying lower and lower toward the ice as you hit it until it finally goes right through. This will shatter several blocks and then it will start flying around again. Keep hitting it until it starts moving faster and faster. Pummel it a little more and it will die.