I've been fortunate to hunt most of the animals that are in many of your dreams. To name some, elk, moose, caribou, brown bears, black bears, Mt goats, Mt lions, sheep and African game. Every hunt started out as a dream and I somehow made them happen. My advice, follow your dreams if you really want to live them. Some of those animals aren't that expensive to hunt so stop dreaming and go!
What I dream about mostly is hunting all North American sheep. With the cost associated with those hunts it is something I know I will probably never do. But I'm not ruling it out quite yet because we all have dreams and that is mine.