I had an idea for this a while back, but I'm not sure how many people would buy it. My thoughts didn't involve an RPG, but sort of a free-roam game kind of like the Spider-Man ones (side missions, story missions, etc.), where completing the story objectives in different ways allows the game to recommend special weapon/armor/physical upgrades based on your hunting style. Then you'd do the side missions to earn things that don't quite mean as much, but look cool (costumes, decorations, honorable titles, trophies and trophy necklaces).
I'm with strigoi on the "no RPG" thing, and for the same reason; we still want some mystery to the character and if we expanded the universe through the game rather than actual movies (yuck), it wouldn't be as cool. I think the best thing to do here would be a more open and polished version of Concrete Jungle. Bigger cities and areas with non-linear gameplay, plus the option to choose or deny missions so that in-between your assignments, you could practice your hunting skills at your own leisure the way you want. Then when you actually put those skills you played with to the test in the story, the game will record it and suggest how you can 'pimp' out your Predator accordingly.
Maybe even the option to travel to multiple planets would be neat, since the story might take you back and forth between Earth and the Homeworld. So it's basically the entire universe of the character based only on what we've seen on the big screen, but with the freedom to navigate through it how and when you like.
Lastly, third-person is a must IMHO. One of the best aspects of the Predator (and what makes Concrete Jungle still relevant) is the acrobatics. You want to see the armor and weapons you've earned in action, you want to see your customized hunter doing his thing. This also improves gameplay, since bringing it out to third-person greatly increases the number of things you can do, as opposed to first.