Let's look at the motivations behind amassing all that cultural capital of gamerpoints and completion percentages.
Obviously the heart of the matter is that achievements let gamers share evidence of their skill and persistence with a game, and overall gamer status, as, e.g. the total amount of gamerpoints at Xbox Live. Thus they have to do with players' emotions of pride - 'fortunes-of-self' in terms of emotion theory. Or, with admiration and respect of others. In summary, achievements give concrete evidence for bragging rights.
Achievements are also a form of extraneous goals to the game, i.e. they seldom are tied to the theme/fiction of the game - achievements give another meaning to player actions, results, and goal resolutions than what, e.g., the story of the game.
To keep in line with the perspective of this blog, i.e. emotional game design, one wonders if there could be a way to categorize achievements from an emotional standpoint? It would seem that most of them have to do with the emotion of pride, but there aren't necessarily many more emotional spaces or nuances that achievements would occupy. Peer acknowledged and generated achievements would expand that space.
One reason for this is, that at least for now, achievements and trophies are measured by quantitative means - they are something that the game as a system can calculate and thus keep track of. Qualitative achievements would have to relate to a certain style of play, or to something recognized by peers. Qualitative achievements would be measured by the buzz they create in the community.
To my knowledge, there does not seem to be many achievements like that. Qualitative achievement would also include achievements that change the qualitative nature of the gameplay experience. The one in Mirror's Edge about not using firearms - 'Test of Faith' it's called - comes close in spirit, but it's still down to something quantifiable in the game. Geometry Wars has an achievement called 'Pacifist' (thanks to @lassi for pointing that out), which challenges the player to refrain from shooting at the enemies, i.e. it changes the player's perspective to the gameplay by reversing goals.
These are achievements that display design thinking, instead of simply translating a number of quantifiable player attributes into sets of deer heads on a wall.
My conclusion, in the form of hypothesis:
At present, game achievements and trophies relate to prospect-based emotions only. Qualitative, peer generated achievements would expand the emotional space of gamer communities, such as Xbox Live and PSN.