I think it would be pretty neat to follow a youngblood/right of passage story. Like AVP but minus all the suck. I think if it was played off kind of like the beginning of 300, where you see young Spartans during their life and training in the
agoge, but with Predators. Show the brutality of their training and how merciless they can be. As well as the young Preds constructing their weapons. Follow that for a bit, then have it build up to a "Final Test". Drop the protagonist along with another fresh young Pred or two on a jungle planet somewhere. I would like to see a story where we see them hunting that T-Rex looking creature from the P2's ship. Think Predator meets Jurassic Park. They would be hunting their trophy Alien-Dino-Monster in order to achieve adulthood. They could be faced with some other challenges along the way. Have them get stalked by a group of Velociraptor-type aliens, which could take up a lot of the story. But eventually have them work together to bring down the big prize. Maybe they don't get lazer Cannons until they have proven themselves, so they are forced to use spears, shurikens and wrist blades, set traps, and fight hand to hand.
Have one of the supporting Pred's get killed (late in the story) and have the other supporting Pred be a female. There doesn't need to be a love story developing in the background. Just a story of survival and tribal rights of passage. Finish it off with a small ceremony in their honor, with a few Elders and other Predators there. Not delving too much into their world, or their society outside of the hunt. But see them receiving their shoulder Canons and becoming full fledged Yautja adults.
I think it could be done with a VERY minimal amount of Dialogue. Body language, and mood could go a long way. Possibly some Text at the beginning. A few screens setting up the story. Maybe some subtitles if absolutely necessary.
That's the story I'd like to see. Keep it really, really tribal. Aside from the technology of their ships and weapons and whatnot.
*No Humans in the story at all. A Skull or two kicking around maybe, but NO HUMANS!*
Just my 2 cents.