If you have enough stimpaks on you to hit the 10K mark for the achievement, you can get this without constantly damaging and healing yourself. Just take a nice chunk of damage, then save your game. Turn on Hardcore Mode, which makes stims heal over time like food, if you're not playing it already. Now go to your Pip-Boy menu and just use up all your stimpaks. When you get the achievement, reload your saved game and turn off Hardcore Mode so you can continue with all those stimpaks.
When you use a stimpak like this, its total healing is immediately added to your total for this achievement, even though you haven't received all of the actual healing yet.
Using the Today's Physician magazine and certain clothes to boost your Medicine skill will make this go faster, or at least improve your chances of reaching 10K with your stimpak supply.