1. Barrel
2. Bullets
3. Bedding

All else is just the interface between the shooter and rifle, as d.id already covered. Trigger, stock, optics, action, all are but means for the shooter to steer the barrel, and ultimately, the bullet. But the barrel and the bullet are where it's at. If these two items are not compatible, and of good quality, then nothing else is gonna really matter. A factory barrel can be very good, but many are not. Generally, aftermarket barrels are of better quality. Good bedding allows repeatability with the whole system.
I disagree with all the emphasis on the shooter. The question was "what makes a rifle accurate?", not "how do I shoot a rifle accurately?". Any rifle is only capable of a certain degree of accuracy with a given load, and there's nothing any shooter in the world can do to magically improve on that, without making changes to the rifle.( ETA, or the load.) Either a given rifle will shoot MOA, or 1/2moa, or 2 or 3 MOA etc. Once you reach the limits of the equipment, the shooter can do nothing to improve on that. It can certainly be shot worse at that point, but not any better. I disagree with the comment about putting the best shooter behind the worst rifle and he will outshoot an average shooter with the best rifle. This is nonsense. I consider myself an average shooter. Give me a rifle capable of 1/4 MOA and give Tony Boyer an old beater that can't break 3 MOA, and I'll smoke him every time. Not to say that technique is unimportant, or that shooting is not a skill that can be highly refined; that, too, would be nonsense. But all equipment has limitations, and no matter how great our skills, or how inflated our egos, we cannot ignore that fact. Shooting a good rifle accurately is really not that difficult. I'm not talking about extreme, competition-level accuracy, but the 1/2 MOA that the OP desires. Case in point: a few years ago I was at the range, shooting my stock-except-for-the-stock, model 10 FP. I noticed a young man, maybe 15 yrs old, watching me from a short distance away. He seemed very interested. I asked if he would like to shoot, and he enthusiastically said yes. After securing permission from his parent, who was busily making noise over on the pistol range, I sat down with this kid to determine his level of experience. Turns out he had never fired a centerfire rifle before. No problem. I gave him a brief talk about safety and rifle shooting basics, and he fired a .308 for the first time, at 100 yds. About twenty minutes later, after having all of about twenty rounds' worth of "experience", he was breaking clay pigeons placed on the 600 yd. backstop, probably two of every three attempts. That's roughly 2/3 MOA at 600 yds, 2/3 of the time. That wouldn't have happened with a rifle that shoots a 12" group at 600 yds. And I seriously doubt, that any shooter could take that particular rifle that he was using, and do much better than 1/2 MOA with it. Maybe .4 MOA. Yes, the shooter matters, but the inherent accuracy of the rifle itself is paramount, and improvements due to technique are incremental, assuming a basic level of competency.
So to the OP, if you are shooting a Trophy Hunter at sub-MOA, but desire sub-1/2 MOA, I'd say you are already probably pretty close to the limits of the rifle, but there still may be room for improvement. Will your rifle ever shoot "one-hole groups" as-is? Probably not. 1/2"? Very possible. But if you want much better than that, you will probably be looking at improvements to the rifle. That being said, there's certainly nothing wrong with practice, especially carefully thought-out practice.