Glimmer: There are many ways found for this world. One is to use the Double Jump Glitch to reach a boundary and head towards the other garden.
Summer Forest (Swimming): To avoid paying Moneybags to learn how to swim, just use the cheat that grants you all your abilities. This will also allow you to avoid paying for the other two abilities later on (You can also use the Double Jump Glitch, though it's not recommended, since you will not be able to complete Sunny Beach and Aquaria Towers. You can, though, use it to skip paying for climb and you won't miss anything).
Summer Forest (Accessing Aquaria Towers): Either use the swim in the air glitch and swim over the wall, or use the double-jump to jump over the wall. Make sure this is the last world visited for Summer Forest, otherwise you'll be stuck. If that happens, just reload the game.
Aquaria Towers: Activate the Swim-in-the-Air glitch, and just swim over to the button in the third area with a button and press it. Avoid pressing the other buttons or talking to the seahorse with the talisman.
Crystal Glacier: Before Moneybags, there are some mountains. Use the Double Jump Glitchto reach a strange structure, then use the Double Jump Glitch once again to glide to the other side.
Magma Cone: Use the Double Jump Glitch to get on the boundaries, then glide to the end.
Winter Tundra (Accessing Canyon Speedway ): Use the double jump glitch to jump on top of the mountains, and glide below the portal while being outside of boundaries. This can be combined with swim-in-the-air glitch or dashing at the end to make it easier to reach the invisible portal.
Year of the Dragon
Sunrise Spring: It's possible to access Sheila's Alp without speaking to Moneybags. Just use the superfly powerup to reach the top of a tree, then glide to the world boundaries, fly underneath the pond, and use headbash to active the Swim-in-the-Air glitch (requires timing). Swim underneath the portal, and if you reach the right part, you'll enter Sheila's Alp.
If you manage to complete this world, all the sub-areas with Sheila will be activated, though the sign will still say that Sheila has been captured. In Spooky Swamp and Desert Ruins, there will be no comment on the sign.
Cloud Spires: To avoid paying Moneybags, jump onto a cloud near where Nimbus and Cirrus are, and glide around the edge of the cloud until you find yourself in a portal. Just exit it, and you'll be near where Fluffy is.
Midday Gardens: To enter Sgt. Byrd's Base, you'll have to use the Swim-in-the-Air glitch to swim underneath the portal. Avoid swimming near the cage, otherwise you might get stuck behind Sgt. Byrd. If that happens, reload the game.
Like with Sheila, if you manage to complete this world without freeing Sgt. Byrd, all sub-areas with him are unlocked.
Spooky Swamp: Get on the lantern nearest to Moneybags, stand on the ledge and glide towards a tree. You'll be in front of Sheila's or Sleepyhead's Challenge Portal if you did it right.
Molten Crater: Since there is no other way to enter the area with the thieves, this place cannot be dodged, but can be completed after defeating the Sorceress and chasing Moneybags in Midnight Mountain.
Icy Peak: The area with Nancy can only be accessed by paying Moneybags. This only applies to the PAL version, as it is possible to dodge him in the NTSC version. You can also defeat the Sorceress, chase Moneybags, and complete it.