The Mexican Ice Badge should be a hard badge; it took me nearly 5 hours before I could get it. Here's a tip: Try to hold down the up arrow as much as possible. The key is to try and slide your opponent into a wall (easiest if it's a diagonal slope to the left) or to tip your opponent off a platform (by carefully tapping and holding the arrow key until they fall off).
The easiest way to make sure no one dies is to lure all the humans to the fireplace room (don't scare them completely on the 2nd and 3rd floors, if they're screaming their lungs out then they might suicide), then spam the "down" action on the mirror to scare them out of the house.