A stray click later, and my thoughts of making it to 85 without dying were shown to be... somewhat overly ambitious.
Which led me to think, "Oh, wow. Too bad. They should add an achievement for making it to 85 without dying!"
... which, in turn, led me to think, "Hmm. Are there any achievement - aside from feats of strength - that you can lock yourself out of completing?"
An achievement for hitting 85 without dying would meet this criteria. Run into Hogger? Smish! No way possible to get that particular achievement. Another example would be a "run dungeon X at less than level Y". Which would be an interesting indication that you've done something challenging... except that once you hit level Y, that's it - the achievement isn't possible for that character any longer.
After spending a furious 15 seconds thinking about it, I'm pretty sure the answer is "no" - there aren't any regular achievements that you can't complete, eventually, on any character you might want to do them on. Which is pretty darn impressive, if you ask me. If there's a non-FoS achievement in the game, you can get it, period. It might take you forever and a day to level to the point where you can run that dungeon, or fish up Mr. Pinchy, or farm up that last pet, or win enough BGs to get that mount... but that's it. With enough effort and/or assistance, you can acquire any regular achievement in game.
Am I wrong here, though? I know about quite a few of the achievements, and while I'm pretty sure that I've looked them all over at least once or twice, I may have missed something.