Note: this glitch requires a controller that allows pressing both Left and Right on the D-Pad simultaneously.
During the introductory level of the game, grab a certain number of Coins, depending on where you want to go. 0 or 9 Coins brings you to Extra 1, 1-8 Coins brings you through to that level of World 1 (i.e. 5 Coins = World 1-5), 10 Coins to the Bonus game for World 1, 11 Coins to a glitched level, 12 Coins to the intro level, and then 13-15 Coins brings you to World 2-1, 2-2, and 2-3 respectively. (These values loop based on 16, so you can still do this at higher Coins if needed. For example, 37 will bring you to World 1-5, as 37 divided by 16 has a remainder of 5.) With this achieved, use Start and then Select to leave the level and return to the map. There, press Left and Right together, then an less than half a second after begin holding the A Button. The cursor will glitch up a little, but you will soon transition to the named destination level.
What this glitch will do is essentially make 1-2 into the level you've chosen. It is recommended to only do this with World 1-2 to 1-8 because of this. If you go any further, you won't be able to play normally. Upon resetting the game and reloading, you cannot play World 1-1 or any levels you've actually skipped, though the levels you've played will act normally.