I was halfway through Family Secrets, just about to dig up the sculptor’s wife's grave, having used no hints or skips, when I noticed that, wait a minute? The achievement for not using a hint in a scene never triggered! Something’s not adding up!
Here’s the problem: this game’s achievements are meant to trigger in the Snark Busters games. In other words, it does not matter what you do in the 1000 Doors games. At the time of writing, I've only finished Family Secrets and the three Snark Busters games, and I still have all achievements.

General guides
These games have been out for a decade, so their guides can be found on casual game websites. Several will be linked here:
https://www.bigfishgames.com/blog/walkthroughs/snarkbusters.html
https://www.bigfishgames.com/blog/walkthroughs/snark-busters-all-revved-up.html
https://www.gamezebo.com/2012/06/16/snark-busters-high-society-walkthrough-cheats-strategy-guide/
If you run into trouble in those games, the House of 1000 Doors games have included strategy guides.

Welcome to the Club!, All Revved Up, and High Society trigger at the credits of their respective games.

Bundle Master
The title is wrong, actually!! This triggers when you have all three Snark games done; the H1000D games are irrelevant to this. I played High Society last, so it’s triggered at the credits at the same time as the completion achievement.

These require specific feats, which you'll have to go out of your way for.
If you miss one, these games aren't too long. My playthroughs come out to around two hours a game.
Welcome to the Club is the easiest of the bunch, so I would use that one. I got all six of these in one playthrough.

Glued to my Chair
Spend an hour in a Snark Buster’s game. Impossible to miss.

Elementary, dear Watson!
Complete a Snark chapter without hints. For me, this triggered after the first game’s tutorial, stealing the police captain’s hat.

Less than a Minute
Complete a minigame in less than a minute. The element sorting minigame in the first game, second chapter’s gazebo is very quick to solve, so that’s where I got it.

Film Critic
Every Snark Buster level has a TV with a news broadcast on the ongoing plot. Watch all of them, and this will trigger at the credits.

As Easy as Pie
No minigame skips for a whole game. In Welcome to the Club, most of the puzzles aren’t too hard. The most complicated one, the dial puzzle in the railway cart, has a written out solution in the first game’s guide. This will trigger at the credits.

Everything is Possible
No hints for an entire game. This will require some keen eyes, or just using the linked guide. This will trigger at the credits.