On 7 Nov 2020, the game got a major update and the achievements have been replaced with new ones.
The walkthrough remains fully valid, but the coconuts (Chapter 1) / umbrellas (Chapter 2) / textbooks (Chapter 3) and floating devices (Chapter 4) have been replaced with drawings, each of them granting a new achievement. The locations are exactly the same and being close to a collectible is indicated with a sound.
This is why in the screenshots below (those that explain the paths you need to take) you will encounter these terms; please read them as "drawing".

Scare the poop out of a piggy
How to: Repeatedly chase any pig you encounter in the game (make him run away from you for 5 times). This achievement can also be obtained in Chapter Two.

When you reach the crossroads marked with a round patch of grass, move left, uphill (instead of continuing to the right, downhill)







The second drawing is located in the small hut next to the suspended bridge.







After the waterfall, you'll see another small hut. The third drawing is on the table.





Long after the rows of huts, you'll find yourself in some sort of opening with 2 possible directions: left will lead you to the 4th drawing, right further in the game.






At the lake, follow the path on the right past the waterfall until you reach some huts; the drawing is in the one with a small bench outside.







In order to progress to the next segment, you need to find the batteries and fix the radio. Both of these are in the same hut (the batteries are on a barrel inside the hut), right before the end of the chapter.

At the deer statue, first go left until you reach some chain, then immediately turn right and head to Danny's Café. On the table you'll see a note.


Pick it up and go back to the deer statue, afterwards head towards the playground. Pick up the bunny toy.


Go back to the deer statue, and then to the cafe behind it.

After around 2-3 minutes into the second chapter, you'll reach a crossroads. If you take a few steps in from the screenshot you'll see that there's a path on the right side past some small red plants. At the end of the path you'll find the 6th drawing.








Go further until you reach a set of 3 huts; the 7th drawing is in one of them, behind an already opened door.







After you cross the 2 bridges and past the little hut, you'll see another crossroads marked with 3 palm trees. Taking the right path will lead you to the 8th drawing.







Go past the stone gate and the cross the stone bridge; the 9th drawing is at the bottom of the tower located on the left side of the stone bridge, after you cross it.





The10th drawing is located in a hut (after you pass the 3 pigs).







Before entering the last hut and listening to the radio, you will need to collect the batteries:

Go to the end of the building, until you reach a room with a chair. Around a pillar there is a crowbar that you need to pick up.


Go back to the starting point. Click on the door to unlock it.


Go further down, until you reach the end. Pick up the bunny toy at the foot of the pillar.

Right at the spawning point, on the right side of the path.





At the base of a sturdy tree on the right side of the path, right after the following text pops up:







Just can’t help yourself, can you?
How to: In order to trigger this achievement, click multiple times on the axe from the picture below:



From the axe, go right and follow the left edge of the map until you find a lonely tree.







Before going ahead to the hut with the radio, make sure to pick up the batteries located on a barrel, on the left wall.





In the house with the radio, on a chair.





Past the hut with the radio go further until you find a small village on a lake. The drawing is in one of those huts.







Pick up the paddle on the bridge in order to trigger the ending sequence.

Scare the bejesus out of a bunny
How to: Repeatedly chase any bunny you encounter in the game (make him run away from you for 5 times). You'll find multiple bunnies roaming around the center of the map.

The map is a circular area with layered winter platforms; the easiest strategy I found in order to collect all the items needed was to go round the map, hugging at all times the right wall.
However, in the Redux version, you can toggle markers that indicate the locations of the wood sticks (right click).

Here's a YouTube video with a full walkthrough of this part:

After you leave the cave, go towards the water, hugging the right wall of the map. The 16th drawing is behind some rocks.







On the floor of an open cabin, in the center of the beach.







After you pass through the stone arch, head towards the left of the map - the 18th drawing is right at the left wall, a few steps further.







Inside a hut with a fence and stairs.





Behind the last hut of the game (the one with a floating bottle on the side).








Complete the game
How to: Click on the bottle.