Achievements are roughly sorted by world, so you only have to read a single section upon reaching a new location. Some achievements require 2 players - this can be done with a keyboard + controller.
There's a cleanup section for everything else that doesn't really fit in.

Then there's the speedrun playthrough which should be left to last.

None of the achievement are missable because you can reset a level to it's original state if needed.

Long Jump
Long jump: dash and jump!

Simplest achievement. Dash and then jump immediately. That's X then A on controller.


High Jump
High jump: heavy dash and jump!

Same thing as above, except hold dash. So hold hash and then jump immediately. Hold X then A on controller.


First Steps
Finish the tutorial (no skipping)

Don't skip the tutorial when prompted.

Fashionista
Buy every costume

The shop is immediately right of the tutorial portal in Boxling Square. Buy all the constumes of the achievement. You will need every gold cube from every level to be able to afford everything.



Costume Change
Put on a new outfit

Buy any constume from the shop and wear it from the pause menu.


Retro Gamer
Play every game in the arcade

Requires 2 players. There are 4 arcade machines to find, one in each world. See below for the locations of each arcade machine. The arcade itself is up from the shop. Head inside and play each game once for the achievement.



Companion Cube
Carry an item through 10 consecutive rooms

Take any box and bring it through a bunch of rooms. Can easily be done with the box outside the arcade and circling around Boxling Square with it. I assume you can't put down the box either.


Explorer
Explore all of Boxling Square

Visit all the rooms of Boxling Square. I don't think collecting everything is required for the achievement, but you'll need to collect everything another achievement anyway.

And Now What?
Bounce a trampoline... on another trampoline

Easily done from the room left of the big frog. There are two consecutive rooms with trampoline.



Sunshine
Open every beach umbrella

"Open" is a bit misleading as umbrellas are already open by default, and the achievement unlocked for me just by closing them. Dash into an umbrella to open/close it.
There's one umbrella in Boxling Square.


The rest are in the first portion of Frogipelago (between the first and second frog).



Lighthouse Keeper
Open the bonus route in Frogipelago

You'll pass this obvious star icon on the way to the final frog. Unlock it to open the bonus route.



Pile Up!
Make a pile of 5 boxes or more


Pile Upper!
Make a pile of 10 boxes or more


Pile Uppest!
Make a very big pile of 20 boxes or more

This can be done in the bonus route in Frogipelago. when you reach this room, carry one box with you to the next room.

There's 6 boxes on this screen.

And there's 11 boxes on this screen. 9 regular, 1 sticky, and 1 trampoline box.

Take all the boxes to the second screen and build a stack of 18 (make sure the trampoline box is on top). Remember start stacking from tallest to shortest as you can't stack on top once the stack reaches too high.

Spawn in a second player and throw the stack on them. Pick up the second player to create a stack of 20 (including yourself).

If you have 2 controllers (plus keyboard), the room with the 2nd spider at the end of the tutorial has 17 boxes. This room makes it even easier.


Clean Space
Throw a pile of 10 or more boxes into the water

Can be done along with "Pile Uppest!".


A Big Mess
Destroy a pile of at least 10 boxes

Can be done along with "Pile Uppest!". Dash while holding a 10+ stack.


Concert
Listen to a musical performance by some slimy friends

Story achievement. Unlocks after rescuing all four frogs and reaching the big frog at the top of the world.


Ribbeat
Complete Frogipelago 100%

Collect everything in the level then enter the portal at the top of the world that goes back to Boxling Square.

Hey, Come Back!
Build an autonomous flying box

On your way towards the second switch will be a simple room with a flying box.

Take it to the following room and toss it on top of another flying box.



Movin' Out
Move the wall of boxes in the cave to another room

Between the second and third switches you'll reach the following room with a wall of 16 boxes.

Enter from the left side. Use the flying box to fly over to them and grab a stack and use the second (not pictured) flying box to fly to the lowest level. Toss the flying boxes into the water (if not already) and jump into the water to respawn on the left side. Repeat three more times until all four stacks are on the lowest platform, then carry each to the next room.


Spelunker
Open the bonus route in Citizen Cave

You'll have seen this on the way to the second switch. If not, enter the portal with the star near the beginning and follow it to the next room. Unlock it to open the bonus route.



Cinema
Watch a movie with upside-down friends

Story achievement. Unlocks after turning on all the lamps in the projector and returning to the cinema.


Movie Star
Complete Citizen Cave 100%

Collect everything in the level then enter the portal in the projection booth that goes back to Boxling Square.

Squash Smash
Smash every squash in the game at least once

There are 10 squashes in one room in Boxling Square.


And the rest are in Citizen Cave. There's two in the stands near mother hedgehog.

Bunch in the stand behind the well.

Around the first gate. There's one hidden behind the sign.

Two in the lower right corner here.

Along the bottom of this room.

There are more after this quick achievement...


You Monster
Do something horrible...

After rescuing the baby hedgehog, toss it off the edge anywhere. Must be done before returning to the mother hedgehog.


Contining with the pumpkins. After the mother hedgehog moves further in the level, there's a row along the side of this room.

Room after the previous.

As you make your way towards the fireworks.

Last bunch is near the explosive box used to light the fireworks.



Climber
Open the bonus route in Forest Fair

On they way to rescuing the baby hedgehog is path that leads to the bonus route.



Fireworks
Watch a fireworks show with spiky friends

Story achievement. Unlocks after setting off the fireworks.


Birthday Boy
Complete Forest Fair 100%

Collect everything in the level then enter the portal near the fireworks that goes back to Boxling Square.

Statue
Strike a pose on a pedestal

The rooms leading up the upper galleries of the theatre have pedestals. Some pedestals have boxes on them. Remove the box and stand on the pedestal for a few seconds.



Suit Up!
Open the bonus route in Feather Theater

The bonus route is in the backstage area while getting the second prop. Find the rest of the tape rolls and unlock it for the achievement.



Theater
Watch a performance by colorful friends

Story achievement. Unlocks after completing the costume for the bird and returning to it.


Curtain Drop
Complete Feather Theater 100%

Collect everything in the level then enter the portal on the stage that goes back to Boxling Square.

Arachnophile
Scare every spider in the game

There are 8 spiders in the game. The first two are in the tutorial.


One is in Citizen Cave. After going the through the portal with the star.


One is outside Citizen Cave in Boxling Square. Need to finish Citizen Cave first.


Two are in Forest Fair. Near the beginning.


Last two are in Feather Theater. After going through the portal to backstage.



Piggybank
Pick up every collectible in the game

Collect all the gold boxes in every level including Boxling Square. You'll need all of them to afford the every costume for 'Fashionista'.


Fish Food
Fall to your doom 100 times

Simply load any level and keep dropping off the edge. Can be idled if you rubber-band your controller or something...


Hydrophobic
Complete a world without falling

It's unlikely you'll unlock this the first time through a level. Use 'Restart Level' on the pause menu to reset the level to the beginning and try again. All collectables will stay collected. Personally I did it on the third level.

Faster Than Lightseed
Finish the game faster than the Seed By Seed record

First of all, you need to unlock Speedrun Mode by collecting all four Timer Pieces at the end of each bonus route in the four main levels. Refer to the sections above if you need to know where the bonus routes are.

Turn on the speedrun timer in the options and start a new game. The time to beat is 36 minutes and 10.8 seconds. The timer must be on when you finish the game for the achievement to unlock.

Some tips:

• This run by Le Kinkss shows some useful skips: https://www.twitch.tv/videos/957907296. The more difficult skips (like jumping on a bouncing box) are not required.
  
• Remember you can high jump up ledges two boxes high.
  
• Long jumping is fastest, but even simply dashing seems to be quicker than regular running. Dash whenever possible.
  
• Quitting to the menu/desktop will save the current time and room you are in. This is good for creating a 'checkpoint' before a difficult room or skip.
  
• Force quitting (ALT+F4) will not save the game, hence you can force quit to fall back to the last checkpoint created.
  
• My times:
  
  • Frogipelago Exit: 6:05
    
  • Citizen Cave Exit: 15:08
    
  • Forest Fair Exit: 22:12
    
  • Feather Theater Exit: 31:13
  I finished with just under five minutes to spare so you can be a minute per level slower than me and still make it.

Boxling
Unlock all other achievements

Self-explanatory. Should unlock when everything above is completed.