Laying here with some back pain, I figured i may as well put some thoughts down for anyone interested in how I craft achievements and my own personal desires are when both playing and crafting.
Let me get one quick oddly specific thing out of the way: I am 100% on board with retro games (RetroAchievements obviously falls within this camp) having tutorial achievements. I don't think modern games need them (generally), since the in-game tutorial accomplishes the goal of training a player. Older games, especially from generation 1 to 3 (and a bit of 4) relied heavily on their instruction manuals to explain game rules, and even those were typically lacking in some way. Having some achievements there to inform players is an effective way to teach newcomers that don't necessarily feel like tracking down a scan of a manual that may not even help.
To get even more oddly specific, I often include 0-point exposure-based achievements for causing a Tilt penalty in pinball games that I develop sets for. You may ask "Why? Doesn't that encourage bad gameplay?" My argument is no, it doesn't, and in fact it exposes a mechanic to new players that they otherwise may overlook. Many new players to pinball don't know about "nudging" as a mechanic. Video pinball doesn't always feature nudging, but more often than not it does. Sometimes, said nudging is just like real life pinball, where if you do it too much, you get a Tilt penalty and it forces your ball to drain. As a pinball aficionado, I of course know nudging is crucial to consistently achieving high scores and completing table events as effectively as possible. A newcomer wouldn't know this at all. By having an achievement that exposes the Tilt penalty, it in turn exposes the nudge feature, which acts as a more "meta" tutorial, as the player will have to infer from the penalty that nudging is actually a good thing; so good that the game will penalize you if you do it too much. I think it's helpful for pinball wizards too, because if I craft a set WITHOUT a Tilt achievement, it means there isn't a Tilt penalty. In these cases I often go out of my way to create custom nudge-based challenges to further expose the nudge feature, and help new players discover the joy of pinball (see: https://retroachievements.org/achievement/346131 among others).
Getting back to generalities, I also really enjoy the concept of "novel" achievements, though some may find the concept frivolous or even arbitrary. I've talked about it before, but the "Pacifism" achievement for Geometry Wars was the first time I ever had an achievement encourage me to play a game in a way that was actively counter intuitive to the main point of the game, and despite that, I had a ton of fun doing it! Similar challenges would be to beat a certain level in Sonic without collecting rings, or Mario without coins; a regular playthrough would more or less require you do so, but to actively avoid them forces the player to reevaluate the entire level almost from scratch. When you love a game like that, and have played it to death already, a novel achievement like that can inject new life into it and allow a player to have fun with it all over again.
Of course there's straight forward achievements for progression, Easter eggs, and challenges. These are both necessary and expected; players want to show off that they beat a game, and they'll feel discouraged or even uninterested if the achievements don't respect their time investment. This is something some developers butt heads over; some feel it best to minimize achievement spam for things like beating individual levels or collecting individual collectibles, and in some cases, that makes perfect sense. Beating 1-1 on Super Mario is hardly an "achievement." So in those kinds of games it becomes the norm to expect achievements per world instead of level. Seems fair enough. However, as I've gotten older and my time spare time has shrunk more and more, I better appreciate the idea of "popcorn" achievements; having a reward to mark my progress for the limited time I have encourages me to come back and keep trying. If I see a set that only rewards achievements for hour+ investments at a minimum, in games where levels are about 5 minutes a piece or so, I probably will look for something else; I don't necessarily have an hour to invest to hit that milestone. I don't think all games should do this, mind you, including Mario or Sonic, but for context, those games can be beaten in an hour. For multi-hour games, with save anytime features, I think popcorn achievements work best.
Expanding on that, I think popcorn achievements help developers be more creative with individual level challenges. If you evaluate every level individually, you are more likely to have a novel idea about that level, which can lead to lots of fun.
I'm starting to fade now, but I'll edit this and add more over the coming days. I'd like to talk about my own personal dislikes with achievement design, as well as some of the unavoidable issues with the entire concept.