as an example, see this forum's own zaratustra's game eversion; its achievements on steam are interesting:
http://steamcommunity.com/stats/Eversion/achievements92% of people beat level 1
86% beat level 2
84.8% beat level 3
64.6% beat level 4
63.7% beat level 5
61.9% beat level 6
54.6% beat the game in the normal way
29.9% got the best ending
just from looking at that, it's obvious that level 4 is the hardest level, with a drop-off of 20.2% of players who beat level 3 but not level 4. this is followed by level 1 (8% drop-off) and the final level (7.3% drop-off). for the first level the effect may have to do with some people who own the game not even bothering to play it, however, so that can probably be discounted
I didn't know this about the achievements paradigm. But I think you need more than one dimension to form this sort of conclusion. If you don't factor in deaths, the drop-off (at any point) can be explained by people getting bored and not continuing – a
low death rate followed by a sharp drop-off would also show you that – which is just as likely when the drop-off occurs at the end of level 1.
Oh wow. That explains why so many games give me dumb achievements for completing a level...probably also just designer laziness (I've been guilty of this myself), but that is a very good use for achievements. But then again, on some platforms (iOS) you could just have it send you data every time someone beats a level.
I would hope once the game leaves beta testing this sort of thing would be unnecessary.