I like to think there are three types of achievements.
Plot-linked achievements, which would be along the lines of "obtain your xth badge" or "save [recated] at Meteor's base in [redacted]," or following different story splits, with a final one being "beat game"
Challenge achievements, which would be along the lines of "defeat Ditto-Arceus without items & without any of your pokemon fainting." Exaggeration, sure, but that's the gist.
Tedious achievements, which are time-sinks and/or driven entirely by RNG. You can spend all of 5 seconds to come up with your own examples for this one. Below, I have listed all that I thought of for this... in the span of one minute. Note the recurring themes.