I just finished all but one achievement. Empty pockets is a pretty serious no-life achievement, which with everything else completed I have at 1%! So extrapolating it's going to be another 99 months to complete that...
I think the achievements actually hit a decent spread from trivial (i.e. you will get this easily if you just play) to somewhat grindy but not too bad. Numerous hero achievement are neat in that they do highlight hero mechanics that I suspect are underused, or require the use of the kit in the correct way.
I felt that particularly bloodspikes meal one was probably too much, with stinkeye's being close.
Gabby's achievement was good and I had to actually plan it out to get it to go after a few tries.
My favorite achievement is Improvised Weapons (kill 5000 minions with environmental traps) because it really encourages to look at maps in a new way (I discovered that there are way more environmental traps out there than I had noticed before!).
On the down side, achievements suffer from the same effect as daily quests in that if a kill is required it does need a hero kill blow. This is particularly noticable with So Bossy (kill 500 bosses). This is also the second most grindy achievement after Empty Pockets, so allowing for trap kills to count will be helpful.
Overall I think a few more specific hero-centric achievements would be neat. Some heroes don't have achievements yet and some heroes could use achievements that highlight particular ability combo plays (not unlike gabby's).