First off, I recommend doing the huge grind and upgrading all the powerups for the Fully Loaded achievement, then grinding even more to buy a metric bucketload of continues before going for the Endless Run achievements (about 60 should be plenty, I ended up using about 20).
- Sidenote: Grinding the friend challenges was horrendous. Doing it on a laptop, I wish I had thought to set up a macro to grind a story mission beforehand and left that running for a while. For the sake of sanity and social life I'd advise you do.
Of the Endless Run achievements this is probably the one that will take the longest to get to, and if you're trying for all of them in one run this is the one you should be counting as you go. But given the glitchy nature of this game I would strongly encourage you to split them up (I ended up getting the distance, coins and power-ups first in Alpine Pass, then the rest in Grasslands). Four times I did 30 minute runs getting all the achievement goals, and each time when I died it crashed before triggering any achievements. I guess firing them all off at the same time was too much for this games itty bitty brain.
(15/08/13) - The game has been updated since I posted this solution and may no longer be as prone to crashing. But I still wouldn't take that chance.
The levels generate turns and power-ups somewhat randomly - what worked for me may not hold for you.
From completely unscientific observation I'd say that the Grasslands level is best for the treasure chests, they just seemed to come a little more often than the Canyon, and a hell of a lot more than in Alpine Pass. The achievements only trigger at the end of a run, so once you've counted your 8 chests I'd say die at the next opportunity - you'll likely have the 60 turns and 35 destructible targets for the other achievements, and the longer your run the more chance you give the game to crash.
Once you've died, don't worry if you don't get a notification of the achievement. As long as it doesn't crash, the achievement badge will be waiting for you when you get back to the main menu.
(15/08/13) - As Sashamorning points out, the most useful power-up is Ghost Mode. Grasslands seems to be have plenty of them and, if you've leveled Ghost Mode up, you should be able to string together long periods of invincibility.