One of the fastest way to obtain ten Darkmoon Prize Tickets is by doing the quest “Test Your Strength”, which you can get from Kerri Hicks, the strongest woman in the world, at the Darkmoon Faire.
You do the quest by killing 250 creatures that offer experience or honor WHILE having the Darkmoon Field Guide with you. (I forgot that once, and couldn’t understand why I didn’t gather any trophies.)
Every time you kill such a creature, you’ll automatically collect one Grisly Trophy, and you’ll see them turn up in your bags.
You don’t have to finish this quest the same day as you get it. You can even take it at one Darkmoon Faire and turn it in at the next, one month later, and gather Grisly Trophies between the Darkmoon Faires.
But if you want your ten Darkmoon Prize Tickets fast, and if you’re high-level (90 is good, but you can do this before), then you should head out to two areas, where there are plenty of mobs, easy and fast to kill, and you’ll have your 250 Grisly Trophies in no time.
You’ll find a lot of low-health creatures swarming on both sides of the boarder between Dread Wastes and Valley of the Four Winds.
In Dread Wastes, in the upper Eastern Quadrant close to the Valley of Four Winds, you’ll find swarms of Sapflies, each with a health of only 16,348. Find all the swarms you can and kill them. http://www.wowhead.com/npc=62386
Then cross the boarder to the Valley of Four Winds, and seek out the Zijin Hollowfly swarming in the Paoquan Hollow. http://www.wowwiki.com/Zijin_Hollowfly
Kill all the Zijin Hollowfly you can find, and go back to Dread Wastes. A few trips like that, and you have your 250 Grisly Trophies and can turn in “Test Your Strenght.”