This guide won't help much in giving puzzle solutions, I recommend using the Official Forums:
http://forum.caravelgames.com/userfile.php?f=/11/71/0&BoardID=1#611/3715/0/0
There people on there are a million times smarter and have provided help for most the rooms already.

I will say though that you should complete the other DROD games first before tackling this one.

DROD: The Second Sky's achievements are relative simple. Nothing is missable, as the game has a "restore" feature that allows you to jump back to any previously visited room. There's one pair of achievements that you have to restore for.

I didn't really know how to organise this guide, so I've sorted everything by area, and in the order they're unlocked/visited.

These unlock as part of the story.

• My First Roach
  
  • Kill a man-eating dungeon roach

• Learned the Truth
  
  • Receive an answer from the Truth Vessels

• Threat Located
  
  • Complete Chapter 1

• FWOT Fighter
  
  • Complete Chapter 2

• Survivor
  
  • Complete Chapter 3

• Multiple Undo
  
  • Complete Chapter 4

• Doer of Science
  
  • Complete Chapter 5

• Forward to the Past
  
  • Complete Chapter 6

• In Hot Pursuit
  
  • Complete Chapter 7

• Soporific Savior
  
  • Complete Chapter 8

• Going Nowhere Fast
  
  • Complete Chapter 9

See the "Ending" section and beyond for the remaining storyline achievements.

There are several types of optional items which unlock new areas.

There are 2 key cards to unlock new areas in The Rooted Hub. They're found in:

1. Training Hall 2N1W (unlocks Gentryii Grounds)
   
2. Frozen Wood Entrance (unlocks Explosive Storages)

You can first learn about these in The Rooted Hub at the very end of chapter 1. Basically Arky has made 8 rooms scattered all over the game and solving all eight rewards an achievement. They're located in:

1. Forbidden Underpass 1S2E
   
2. The Scorching Path 6N
   
3. Security Gates 1S4W
   
4. Security Gates 1S5W
   
5. Security Gates 4N3W
   
6. Forgotten Shrine 1N1E
   
7. Explosives Storage 3N1W
   
8. Ore Refinery 3W

The earliest you can finish all these is in chapter 10.

• Master Arky-tect
  
  • Completed all of Arky's challenge rooms

There are 3 Harder Questions to find. Finding all 3 unlocks the Good Ending. More info in the Endings section.

1. Seeding Grounds 5N1E
   
2. Arcane Laboratory 2N1E
   
3. Explosives Storage 3N

There are 8 RCS Stamps to collect. These can be used to play puzzles in Lost Central Station (chapter 10 onwards) which unlock new bonus areas. Bonus areas are post game content unrelated to the story. Stamps are found in:

1. The Rooted Hub 2N1W (unlocks Darts)
   
2. Gentryii Grounds Entrance (unlocks Beethro's Mansion)
   
3. Icy Underworld 5N1W (unlocks Flower Bed)
   
4. Seeding Grounds 3N1E (unlocks Raygun)
   
5. Tar Recycling Annex Entrance (unlocks Machine Court)
   
6. Braxian Below Entrance (unlocks Bonus: Developer Commentary)
   
7. On Dawdling River Entrance (unlocks Bonus: Concept Art)
   
8. Hardest Way 5S (unlocks Bonus: Homages and Deleted Scenes)

I'll only list miscellaneous achievements in the "Chapter" sections. Any areas I've not listed don't have achievements.

• Reflective Economist
  
  • Complete the challenge in TH:2S1W
  Self-explanatory.

• Jailbreak
  
  • Complete the challenge in TH:1N5W
  Self-explanatory.

• Who Needs an Audience?
  
  • Complete the challenge in TO
  The challenge is in 6N3E.

• What's a Tunnel?
  
  • Complete the challenge in GG
  The challenge is in 1N6E.

• Take a Breather
  
  • Complete the challenge in SWaRBS
  The challenge is in 1E.

• Daring Architect
  
  • Clear the secret area in SutO
  The challenge is in 1S2W.

• I Love Puffs!
  
  • Complete the challenge in IU:1N
  Self-explanatory.

• 1. RBS x Q
  
  • Complete the challenge in HitF
  The challenge is in 3S1W.

• Slow and Steady
  
  • Complete the challenge in TRA
  The challenge is in 3N1E.

• Minimally Ambulatory Bomb Squad
  
  • Complete the challenge in SM:1E
  Self-explanatory.

• Mimic Manipulator Mastery
  
  • Complete the challenge in SM:4E
  Self-explanatory.

• Enough Aumtlich
  
  • Complete the challenge in EotS
  This challenge is in 1S1W.

• Master Locksmith
  
  • Complete the challenge in EoA:3S
  Self-explanatory.

• Simplification
  
  • Complete the challenge in EoA:2E
  Self-explanatory.

• Frugal Blaster
  
  • Complete the challenge in WBCEND:1N1E
  Self-explanatory.

• Fools Rush In
  
  • Complete the challenge in WBCEND:1E
  Self-explanatory.

• ...There Was Another Way?
  
  • Complete the challenge in S.Ga.
  This challenge is in 3W.

• He Came in Peace
  
  • Step kindly all the way through TLW
  Arriving in peace is required for the story. Leave in peace too to unlock the achievement.

No other achievements.

The game opens up during chapter 10 after going to Lost Central Station. You're free to explore most previously-visited areas, or continue with the story. If you choose to explore, there are several areas with new achievements/side quests:

• Braxian Below
  
• On Dawdling River
  
• Harder Way
  
• Hardest Way
  
• Frozen Woods
  
• Explosives Storages

• The Road Less Traveled
  
  • Touch the secret checkpoint in FW
  This refers to the checkpoint north of the river in 2N1E. You don't need to visit this section when solving the room. This can be accessed from 3N1E.

Now is a good time to do everything in the Side Quests/Collectibles section.

---

Visit the DAA Headquarters to continue the story. When you go to House in the Forest again

• Doily Snatcher
  
  • Be mean in HitF

• Think Twice
  
  • Be kind in HitF
  These achievements are a pair. You can only get one achievement per playthrough if playing normally. Restore to the start of House in the Forest: 1S4W for the other achievement immediately after getting the first.

Upon returning to Archivist Headquarters.

• Plate Mail
  
  • Complete the quest for the plate
  Storyline achievement. This unlocks with or without the doily.

Eventually, you'll be required to return to Older Holding Vats and ask a character a question...

Asking the first (or second and third) question places you on the bad ending path. You are free to change the question at anytime if you ask a bad ending question.

Visiting the Lonely Campsite after asking the question will start the final chapter and play the bad ending. There are no unique achievements to gain from seeing the bad ending.

Getting the good ending requires asking the fourth question. This requires finding all three harder questions. Asking the fourth question automatically starts Chapter 11.

• Spreading the Word
  
  • Looking for hard questions
  Storyline achievement. Unlocks in the cutscene after asking the fourth question.

Chapter 11 unlocks 6 new areas:

• More Fluff
  
• Empty Space
  
• Save Our Surfacers!
  
• Mother of All Roaches
  
• Englos Defense
  
• Constructs Warehouse

Complete all of them to unlock in the good ending.

• Circuitous Route
  
  • Complete the challenge in MOAR
  The challenge is in 1N5W.

• Garbage Packing Machine
  
  • Complete the challenge in CW
  The challenge is in Constructs Warehouse 3 3S1E.

Now go to Lonely Campsite...

• T-Minus One
  
  • The end of the journey
  Storyline achievement. This will also unlock with the bad ending.

• Customer Satisfaction
  
  • Complete the final chapter
  Storyline achievement. This will also unlock with the bad ending.

• The Second Sky
  
  • Saw the second sky
  Storyline achievement. This unlocks only with the good ending.

Collecting all those RCS Stamps unlocked 8 new locations. Now is the time to do them.

• Ballistics Expert
  
  • Completed D level
  Complete Darts.

• Who Ya Gonna Call?
  
  • Completed BM level
  Complete Beethro's Mansion.

• Horticulturalist
  
  • Completed FB level
  Complete Flower Bed.

• Sharp-Shooter
  
  • Completed R level
  Complete Raygun.

• Mastered "The Second Sky"
  
  • Completed The Second Sky and cleared all secret rooms
  This unlocks after solving all the required and secret rooms.

• Super Bomberman!
  
  • Completed Bomberman challenge
  Bonus: Homages and Deleted Scenes 1S.

• Rocketeer
  
  • Completed Roachu Rocket challenge
  Bonus: Homages and Deleted Scenes 1N.