Challenge map isn't as hard as it looks. Got the badge on the 2nd attempt at it. You just have to keep moving. I got 5 flags and upgraded it on Max Damage.
Weapons like Power Ball, Water Balloon and Eggs, once you complete the challenges required for those, and have mastered them...you theoretically never have to use them again.
Ladder Spears do not make good weapons but I mastered it anyway. You can use it for fun if you wish when fighting.
I think best strategy to get lots more enemies launched is to use the swinging weapons or thrusting weapons. I don't know if using guns are the best for it.
Thank you!