Just select a level and let the game run. Personally I've done this with level 1 in world 3 as you die soon after the level starts. You'll keep dying and restarting. The counter for your current deaths in a level also works as a counter for total deaths in this case. Works while alt-tabbed.
Alternatively, if you don't need to use the computer put a weight on space bar or whatever key you have binded for turbo so you'll die even faster. I've unlocked the achievements after approximately four hours of running the game in background.