If you are having trouble getting the hard badge, try this;
Complete ONLY, the following missions in campaign mode. "Mansion Melee" (for the health drain) and "Lava Palaver" (for the homing-missile and the land mine).
Chose a character that doesn't have feet, like Meepo or Spectre. That way, mouse traps won't affect you.
When in survival mode, don't full on attack the enemies, attack from afar with items that you collect. Don't let your opponent get any guns, or it will spell death for you.
The best strategy, that worked for me, was to use land mines. Place one in the middle of the building in the center, and the building on the left. Place a second one in the middle of the building on the left, below the light post. Continue until you have 15 kills.
That got me the hard badge!
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