This one is tough and if you're not carful will require you to restart.
So the game has a total of 6 large levels. The last two of which property damage cannot be gained. So as long as you get to level 5 with under 100k you'll be good.
I would recommend doing this on the easiest difficulty.
The hardest levels by far are the museum and the city where Staypuft is attacking and throwing cars at you. For these parts be VERY sparing in using your weapons. You'll have a full team by your side the entire time. So let them take care of most of the hard work. Whatever they do does not effect your score.
Be careful around cars, one hit can get you upwards of 20k. Artwork in the museum can also add up very quickly.
Only use your weapon when you absolutely need to and this achievement isn't that bad. Just takes time.