It is called spring ahead. Most of the puzzles involve springs. It involves some advanced mechanics, like throwing a spring at a wall and bouncing off of it in mid-air. I doubt anyone will be able to finish it
Solution for each section in the spoilers:
Spoiler: 1st section
Use the spring in front of you to jump up above you. Wait for the first Yoshi to hatch, then hop on. Jump down and grab the spring in your mouth. Jump as high as you can, then spit out the spring at the peak of your jump. If you did it right, it will bounce down to the hole on the right (or close to it). Jump and dismount Yoshi to get up the ledge. Hop on the second Yoshi, then do the same by jumping on the spring and dismounting at the peak of your jump.
Spoiler: 2nd section
This one is much harder than the last section. Jump down to the lowest area and pick up the spring that drops from the pipe. Jump and kick the spring up into the vertical shaft with the Wiggler in it. Make sure that you hit it with the spring (use the doors to reset the puzzle if you mess up). Go left and DON'T TAKE THE DOORS. You need to jump up using the horizontal spring in the left wall. This will probably be where most people get stuck. You need land on the ground underneath the spring and use that to jump. You won't be able to reach it unless you do a walking jump. After you jump, let the spring's momentum knock you to the platform. After you've made it up, run straight across the small gap into the vertical shaft. Pick up the spring you left in there, and kick it up. I try to aim towards the right side of shaft. If you did this right, you should have knocked the wiggler into the area on the right (he needs to be there). Run back to the left and climb up the vine. Jump into the upper area and pick up the spring you threw in there. Using some precision platforming, jump back up and out of the area. Bring the spring to the lower right area and leave it on the ground. Jump on it up to where the Wiggler is. Use the Wiggler as a platform and jump up to the exit.
This section has a secret solution which is MUCH easier. I'm not going to reveal this one, but you should be able to figure it out later since later puzzles require it.
Spoiler: 3rd section
Drop down to the lower area. Notice the springs falling out of the pipes into the pit. You need to grab the vertical spring as it is falling. After you grab it you will need to use it to get the horizontal spring into the small vertical shaft on the right side of the screen. Stand on the left edge of the pit, and neutral kick the spring to the right as it is falling out of the pipe (running kick will be too far). If you timed it right, the horizontal spring will be on the platform at the bottom of the shaft. Jump across, and kick the vertical spring up the shaft, forcing the horizontal spring up with it (if you mess up, use the door on the far left to reset.) If you did this right, the Wiggler that was in the way will be knocked to the right. Jump up to the bottom of the shaft and pick up the vertical spring. Kick it up again to knock the horizontal spring out of the way. Drop down and go to where the Wiggler is. Use the Wiggler to jump up to where the vertical spring is. Pick it up then kick it up the shaft one last time. Jump up and go through yourself. Pick up the vertical spring again and bring it with you to the right just under where the coins are. Drop it there, then use it to jump up to the exit.
Spoiler: 4th section
Drop down the shaft to the bottom. Wall jump these springs up to the top (this might be hard if you had trouble with it in the 2nd section). After you make it up, run to the right and go through the door (notice the ledge above the pipe). We got more springs falling into a pit. Pick up the vertical spring, and go back through the door you came through while holding it. Return to the area with the springs. Notice how another vertical spring is falling from the pipe again. Leave the one you carried with you out of the way on the right by the door (you will need it later). Grab the newly spawning vertical spring and stand on the right edge of the pit. Kick the spring to the left as the horizontal spring falls. You want to land it on the top right donut block. Pick up the spring you left behind and place it two blocks away from the stone block ([]_{}). Stand over on the right and watch the magic. After the vine is released, drop the 2nd vertical spring on top of the 1st one. This should give you enough height to reach the platform above the pipes. Climb up the vines to the exit. You need to be small for the next part, so get rid of any powerups you might have with the spike.
Spoiler: final section
Drop down to the left of the pit. Grab the falling vertical spring and go through one of the doors while holding it. Now you got 2 vertical springs to work with. Go to the right side next to the door and drop the spring right next to the ledge. Grab the falling spring and stand on the right. Neutral kick the spring to the left to bounce the horizontal spring onto the spring right in front of you. If you did this right, it should be bouncing on it just below the left cloud platform. Grab another vertical spring falling from the pipe and jump back to the right (watch out for the spring knocking you into the pit). Drop the spring on top of the bottom spring. This should put the horizontal spring up on the cloud platform. Grab the bottom spring and kick it up underneath the horizontal spring, knocking it further up (if you stand in the door while holding up to kick it, you will go through the door resetting the springs.) Grab the respawning spring (I hope you didn't throw it up with the other one), and use it to jump to the cloud platforms. To do this, you will need to throw the spring against the wall as you are jumping, then bounce off of it in mid-air. Once you have made it up, you will need to kick the vertical spring up (if the horizontal spring is bouncing on it, you will need to act quick and kick it up while it is in mid-air). If you did everything right up to this point, you should have knocked the Wiggler into the area on the right, and you should have no springs with you except for the horizontal one stuck in the wall. Use it to jump up to the last area. Grab two vertical springs and throw them down to the right. Stack them on top of each other and use it to jump to the exit. I hope you have time left, because the pipe leads to an auto-scrolling section filled with coins. Go down the pipe at the end to finish the level.
November 4th. Be ready for the free update with checkpoints and conditional item boxes. ie. Mushroom box if small, fire flower is big as well as special event courses designed by others selected by Nintendo.
I wonder what else is planned in the future.