Instructions
Start the game playing as either Mario or Luigi. Progress through levels 1 and 2, and get a red leaf to gain the ability to fly. Continue to level 3.
Press the "A" button to jump and jump on the last grey box of level 3. Once on the box, hold down on your directional pad for five seconds and you will go into the background of objects.
Run to the end of the level and go behind the black curtain. You'll be brought to a secret bonus, where a toadstool presents you with a treasure chest. Move over to the chest and it will open, presenting you with a whistle. This whistle will go into your items folder and will allow you to advance to further worlds without having to beat other levels.
Go to the mushroom hut before level 4. Choose a chest and receive an item that you can use later in the game. Try not to use any of these items until the final levels.
Skip going to Level 4 and go directly the first castle. Before reaching the door at the end of the castle level, make sure that you have the ability to fly. Jump on the skeleton and move to the end wall by the door. Press the "B" button and run towards the end of the ledge before the lava. You'll have enough power, and you should fly to the top right-hand corner of the screen. You'll be brought to another chest with a whistle in it. Do not use these whistles until you beat World 1 completely.
Complete all of the first world. After beating the boss at the last castle, you'll receive a cloud that will let you float in the sky above everything for the duration of the level. Keep this for the very last level.
Press "Select" to open your items and select one of the whistles once your have arrived in World 2. The whistle will take you to Worlds 5 through 7. Go to World 7. Once in World 7, press "Select" again and use your last whistle to take you to World 8, the last world of the game.
Beat all of World 8. The levels in this world are much harder than any of the others, but if you have enough special items to use you should easily get through the levels fast.
Use your cloud item for the last level of World 8, so that you can fly all the way to the end of the level and pass Bowser. Once you fly over Bowser, land on the giant key and the bridge will collapse so that Bowser lands into the lava pit. You will now have beaten Super Mario Bros. 3.