A guide to completing World 4-2 in Super Mario Bros 2 for the Nintendo Entertainment System.
Cross the Ice
Go to the right and climb the vine, then dodge the many Beezos that fly straight across the screen. You may sometimes need to jump or crouch to avoid them. There are also a few Flurries along the way.
At the end, you find a door on a cloud. Go through.
Cross the Ocean
Beneath your cloud, there is a whale. Fall down onto the whale and you may notice a water spout. Make sure not to touch the water spout from the side, or you will get hurt. But if you ever need to reach a higher platform, you can jump on top of the water spouts from the whales to go up.
For now, you can optionally go to the left to find a whale with grass tufts on its back. The leftmost grass is a Potion. You can drop it on the right side of the flat part of the whale's back, then go through to get a Mushroom from the whale's tail and two coins.
After you exit Subspace, go to the right. Use a water spout to reach the ice block platforms above you and get the Cherries there.
Don't pick the grass on the right. Go to the third non-slippery platform where there is only one tuft of grass. You can optionally warp to a later world using this Potion. If you don't want to warp to a later world, skip to the next paragraph. If you want to warp to a later world, take the Potion to the right, until you can see a vase to the right. If you are playing as Luigi or Princess Toadstool, you can jump or float to the vase. Otherwise, get on the last whale's water spout and jump straight up onto the ice block platform, then make your way to the right until you can land on a lower ice block platform. From there, go left to reach the vase. Then you can drop the Potion on or near the vase, go through the door, then go down the vase in Subspace to warp to World 6-1.
If you don't want to use the Potion to warp to another world, then go left and drop the Potion on one of the tufts of grass, then go into Subspace and pick up as many of the six grass tufts as you can.
After you exit Subspace, make your way to the right, dodging enemies and using whale water spouts to reach the Cherries above if you wish. If you're playing as Luigi or Princess Toadstool, you can jump to the right from the last whale to reach the vase. Otherwise, you have to use the whale water spout to reach the ice block platform, then go to the right from there. Keep going to the right and you will reach a tuft of grass. Pull it to get a Rocket to the next area.
Cross the Spikes
Go to the right and get the cherry behind the ice column. Then, to the right, you see a Shyguy on an Autobomb, but before you do anything, be aware that there is a tuft of grass on the right side of the platform that contains a Potion. If you want to use the Potion to get a Mushroom, you have to quickly pick up and throw the Shyguy so it doesn't hit the Autobomb, then quickly pull the grass to get the Potion so that you can still jump on top of the Autobomb with it before it rolls away. You also have to crouch while the Autobomb rides over the spikes, or you will be pushed off if you're carrying the Potion. If you reach the right side with the Potion, drop it on the ledge with the Porcopos (which will walk off the ledge onto the spikes), then go through the door and get the Mushroom.
If you don't want to bother with the Potion, you can just stand on the Shyguy and then crouch so you don't get pushed off when the Autobomb rides over the spikes, but if the Shyguy is there, you won't get the Cherries along the way, so you might want to pick up and throw the Shyguy so it doesn't hit the Autobomb, then ride on top of the empty Autobomb over the spikes. If you do that, you don't have to crouch when the Autobomb rides over the spikes.
After you ride the Autobomb past the spikes and get past the Porcopos on the other side, go to the right and go through the door.
Red Birdo
Go to the right to find another Red Birdo. This one is on a slippery ice platform, so you will have to be more careful. Red Birdo spits several eggs in a row, and sometimes spits a fireball instead, so pick up an egg, but before you throw it, wait for Birdo to stop spitting eggs for a moment. Throw eggs at Birdo until the Crystal Ball comes out. Take it and go to the right, go through the mask gate, play Bonus Chance if you got coins, and you continue to World 4-3.