Mrs Burke (30) is up against nine other women, mainly from the United States and Canada, to win a hunt for bighorn sheep, mountain goat and black bear, which will be filmed for TV show Primal Adventures.
The winner will be decided by public vote, which closes on January 1.
Mrs Burke said it would be a dream come true to win the event.
She has been hunting in the Leithen Valley, near Gore, since she was 7, working full-time guiding hunts for her family business, Leithen Valley Trophy Hunts, since 1999.
"When I was young, all I ever wanted to be was a professional hunting guide like my dad and chase wild game around the world," she said.
She shot her first animal, a feral goat, when she was 7.
She guides seven months a year, and spends the rest of the year hunting in New Zealand and around the world.
Her stories include losing her toe nails to frost bite, hunting whitetail in America, crossing high altitude mountain passes using crampons, ice axe and ropes, and chasing Dall sheep in the Chucgatch Mountains in Alaska.
She lived in the Canadian bush for three months trapping and eating some of the "nasty animals that we trapped when times got tough".
She has chased game in Africa and water buffalo in Australia.
"I love a backpack hunt. I love the kind of adventure and live for those kind of places [and] animals that have never seen people before. I'm passionate and love what I do. I truly love my life in the outdoors."
