Pretty sure on that "History's Greatest Monster" one you were supposed to keep the Moon alive until the rightmost end of the level and then collect it to kill the Thwomp.
It's also possible to use the star to kill the Thwomp if you don't collect it too early, not sure if that was the creators intention.
I had a plan that I would clear all levels posted in the "Get On My Level" forum but that level was just too much, I can't stand the wind mechanics. Fun level to see the guys struggle with. :)
runehawke's comments