In the first two worlds of the game, you're able to take shortcuts in the form of invisible barrel cannons to skip to the end of every level except for boss stages. This guide will tell you where these shortcuts are.
1-1 (Pirate Panic)
When you see the first Klomp (crocodile) in the stage, jump up onto the barrel platforms he's walking along. Throw your partner straight up from the first barrel.
1-2 (Mainbrace Mayhem)
At the very start of the stage, you walk past a large mast in the background. You need to get to the part of the mast under the platform you start on. This is most easily done with Dixie's helicopter move, but Diddy can reach it with some clever rolling and jumping.
1-3 (Gangplank Galley)
Climb the steps to the left of your starting position. You'll see a bonus barrel in the open; you need to throw your partner off the top of the screen above that barrel.
1-4 (Lockjaw's Locker)
Klomp marks the spot once again. Stand on the platform where the first Klomp is, on the left edge of the crate covered in seaweed, then jump and throw your partner straight up. Alternatively, go ahead in the stage until the water starts to rise dramatically, then go back to said spot and swim into the gap in the ceiling.
1-5 (Topsail Trouble)
Basically the same thing as Mainbrace Mayhem earlier, and easier to reach as well. Don't forget to jump over the goal and team throw for 3 free lives!
2-1 (Hot-Head Hop)
Throw your partner up on top of the cave to the left of the start, then hug the left wall, jump up and throw your partner straight up.
2-2 (Kannon's Klaim)
Play up to the platform containing two TNT barrels. You'll need to get under this platform and touch the bucket that's hanging below the Krusha (muscleman). Again, easy with Dixie, but possible with Diddy.
2-3 (Lava Lagoon)
Throw your partner straight up from the right edge of the first platform after the first seal.
2-4 (Red-Hot Ride)
Make it to the right of the letter K with your partner intact, ride the balloon up the steam as high as it will go, jump up and throw your partner straight upwards.
2-5 (Squawks's Shaft)
To the right of the start, past the banana coin floating above the bottomless pit. Do a super jump by rolling off the platform then jumping midair past the coin. As long as you're holding right you should make it to the last shortcut barrel.
Normally, in order to obtain the Kremcoins which can grant you access to the Lost World, you have to complete the bonus games scattered throughout the game's stages, and defeat the bosses at the end of each world. There are 75 in all, and it can take a lot of work to collect the lot, but what if I told you there was an easier way? What if I also told you that it can be pulled off before you ever even encounder a Kremcoin by normal means?
Before we start, this may seem like the type of playground rumor kids might spread about catching Mewthree or something, but I promise it's real. It just happens to be oddly specific and elaborate.
Go into the first stage of the game, Pirate Panic.
Go right, then drop down and go left into the room containing K. Rool's note. DO NOT get the two bananas just outside of this room! You cannot touch them at any point during this sequence, or you'll have to start over!
Don't touch anything in this room, just enter and leave.
Go to the right and grab the bunch of bananas floating above the first Klomp.
Go back to the room with the note.
Grab the red balloon and leave the room.
Go right once more and collect the same floating banana bunch again.
Go back inside the room to find a floating Kremcoin worth 75 Kremcoins floating above the note. Enjoy your free ride to the Lost World!