This really isn't going to be very easy. That said I have several tips that should help greatly.
-It's best to go for the Destructor achievement before this one. Doing a run through for that achievement first will give you a good clue as to what counts as causing property damage and the value of it.
-Only attempt this on the casual difficulty setting. This allows you to rely on your teammates to handle most everything whenever they are around.
-Your teammates can destroy objects, but any damage caused by them doesn't count against your total. Try to avoid shooting any debris though as sometimes it will still count against you.
-Try only to focus on ghosts when there is nothing destructible behind it. Let your teammates handle any ghosts near objects.
-If you make a big mistake, you'll have to quit to the dashboard to take away the amount of damage. (thanks to those in the comments for correcting me)
-Get fast trapping and slam trapping upgrades as soon as possible. The quicker you can get rid of the ghosts, the less likely something can go wrong.
-Be extremely careful while in Times Square (particularly around the cars) and in the Museum (particularly in the Civil War exhibit). These areas can add to your damage totals extremely quickly.
-If ghosts are directly in front of you on the ground, normally it is safe to shoot down at the ghost's feet.
-While in Times Square, if the ghosts are far above your head, it is normally safe to shoot the sides of buildings at least allowing you to damage the ghosts. (Thanks to TheRickMoranis
for reminding me of this)
-Once you get the slime tether, this should become your favorite friend. This allows you to instantly trap ghosts without weakening them. It also allows you to trap while guaranteeing to not cause damage. This is a great help during the Civil War segment of the Museum.
-Once you beat the museum level and go to island, you can open up freely. Damage from that point to the end of the game no longer counts against you. You also get a short area like this while in the ghostworld version of the library earlier in the game.