When you're hunting a monster and it reaches its sleeping area, standard practice is to let it go to sleep, drop all the biggest Barrel Bombs you can next to the head or whatever other part you want to break, and then have your party's greatsword user/ gunlance/ heavy gunner use the biggest damage attack they can to trigger the bombs and damage the part (TCS for GS, Wyvern Fire for the other two). This can result in an instant part break or even end the hunt then and there if you're lucky enough, especially with a probably placed True Charged Slash from a greatsword, since a sleeping monster takes double damage for the hit which wakes it up.