Leo Daniels holds the official record for this game with 11,165,570 points.
TIPS AND TRICKS
Begin by filling in the box in the lower left-hand corner. Once you've done that, fill in the two boxes (vertically) to its right, then the three to their right, and so on until you've effectively wrapped around the playfield and are back at the first box you filled in. Just repeat this motion until all of the boxes are full.
Filling in boxes two at a time will give you twice the points of each of the boxes. Filling in three boxes at a time (this is done by going over the point shared by the three boxes last) gives you four times points for the boxes.
You can also get points by punching out enemies. If you can punch out an enemy while the ambulance is still on the screen, you get six hundred points instead of the three hundred for just punching out an enemy.