I'm not gonna even read all the responses...Ya wanta hunt in the mountains, avoid injury, hunt, kill, butcher, and get all legally required trophy/meat home. Great!
I'm an Alaskan. I hunt in remote locations and for days on end. I've completed 25 successful Mt. Goat hunts, unknown Sitka Deer hunts, multiple AK Elk, Dall Sheep, Caribou, bears......
My background is as a triathlete and mt bike racer in my 20's.
I find that flexibility and stamina are the most important aspects of a mt hunt. Each hunter is uniquely physically gifted. I am a large man and lean and mean run around at 220. I am not fast! It's all about maintaining patient and safe movement. The most fundamental aspect of wilderness travel is maintaining mental clarity and safety!
Hear that.....it's not big biceps or a tight ass.
You do need physical fitness to avoid excessive stress and maintain mental clarity, after all we're talking about living in the wilderness for days. However that feels to you and your physiology is the question your asking. Set your strategy and hunt goals appropriately. Know your HR and recovery zones. Know your stamina, and stay within your functional limits. Then go apply it. Your hunt doesn't look like somebody else's, and the damn animal doesn't care! Dead is dead! Now be prepared to execute and return home safely to your friends and loved ones with a nice steak on your time with your skills. Embrace the suck and get home safe.
I'm also an MRI technologist by trade. I know injury. Don't over do it! We are human and excessive weights will hurt you and provide me job security.
Here's to many wonderful healthy years of backcountry exploration gentlemen! Cheers from Alaska