Story Achievements
You can't miss these, just keep playing.

• Part 1 - literally just click "New Game"
  
• Part 2 - starts after the murder
  
• Part 3 - starts after getting the Map
  
• Part 4 - starts after making the arrest
  
• Part 5 - starts after getting the 3 requirements for the Will fulfilled
  
• Part 6 (Secret) - starts immediately after Part 5
  
• Part 7 (Secret)
  
• Part 8 (Secret)
  
• Part 9 (Secret)
  
• Last One Out - Watch Credits until the End
  
• *Beephole* - Ransome's Flashback - Talk to Sandy in S&D's Diner (Part 2+)
  
• Out Of The Will - Delores Flashback - Talk to the woman at the Bus Stop (Part 2+)
  
• Secret Meeting - Franklin's Flasback - Enter the Hotel (Part 3+)
  
• Justice - Have the ArrestTron 3000™ arrest the killer
  
• Sky High - Get an Alive (non-Ghost) Character into the Penthouse.
  
• Easy Win - Complete the game on Casual Mode. Note that finishing the game on Hard Mode will NOT unlock this, so you have to finish the game at least twice.
  
• Hard Won - Complete the game on Hard Mode.

Misc.

• Hotel Tourist - Visit every regular floor on the Hotel, not counting the Penthouse
  
• Great Escape - Escape from the sewers. If you rush through Part 2 and get the Map without getting knocked out, you can't get this. So before getting the Map, make sure to have one of your agents explore the alley behind the S&D diner
  
• Well Informed - Read all 17 headlines of the Nickel Newspaper. They are all in the Nickel Newspaper building, but some are harder to find. Make sure to explore the far right and the ones in the middle.
  
• Book Worm - Read 100 Books in Dolores Library. Literally, just keep right clicking them and ESCaping out.
  
• No One Is Home - Listen to 100 Voice Messages. A bit annoying. I took photos of the phonebook with my actual phone, used the phone in Delores Library (though you can use a Hotel Phone or Rey's cell phone) and kept calling, then hanging up (you can click on the top of the phone to hang up). Note that the phone book puts a green checkmark next to people you already called, so that helps avoiding double calls.
  
• Mean Person - Make each of the 5 player characters cry. In the Occult Books store, there are Cursed Eye Drops, which can be used on 4 of them (just trade the eye drops around). For Franklin, I'm not sure if it's naturally part of the story or if you just have to Wail/Moan/Despair for a bit or if it happens if you talk to Dolores while being a Ghost.

Specks of Dust
These can be collected over multiple playthroughs, and both Casual and Hard mode counts. Note that a single Casual playthrough will not yield 75 specks, but you have to finish the game twice anyway for all achievements.

Specks of Dust are grey pixels (1x1) in most rooms outside of Flashbacks. During the game, they may re-appear in rooms already visited - they are random. They don't do anything, it's just a throwback to classic Lucasfilm Games pixel hunting.

• Dust Appreciator - Collect 25 Specks
  
• Dust Collector - Collect 50 Specks
  
• Dust Hoarder - Collect 75 Specks
  
• Messy World (Secret) - Do not pick up any specks of dust during the game. Be aware that during Ransome's hamster-feeding-quest, the popcorn on the ground and the specks of dust look similar, so you might accidentially pick one up. Hooray for Autosave.

Misc. Secret Achievements

• *Beephole* Mime - During Ransome's flashback, push the Mime on stilts in the bottom right in front of the circus tents
  
• Itchy Fingers - Use Ransomes Itch Cream. Found in the Makeup tent after getting control of Ransome as a regular playable character, not during the flashback
  
• Nuke It - In Chuck's Workshop, get the Strange Device (Philipp's Dangerous Dövice) from the shelf, save your game, and use it. Will need to be used several times before Delores finally pushes the red button.
  
• Buried Treasure - Hard Mode Only - In the Occult Books store, pick up the head. Then go to the trailhead, into the forest, and keep using it. It will spin in your inventory and point in a direction. Keep following it. And no, you can NOT dig out the treasure, can't get a shovel.
  
• Plantastic - Hard Mode Only - Grab the Math Trophy from Dolores room and fill it with radioactive waste from the abandoned factory (near time clock 3). Then, use it with Chuck the Plant in Quickie Pal.
  
• *Beephole* Redux - During Ransome's Ending (Use the "Sorry I was a ♥♥♥♥"-card on Sandy), insult the audience

Location of Strange Device/Philipp's Dangerous Dövice for Nuke It:

Location of Navigator Head (for Buried Treasure) and Eye Drops (for Mean Person) within Occult Books