Okay okay here's a comic book crossover pitch. Stick with me on this one.
Predator vs Terminator
It follows from the first two movies as a sort of alternate timeline thing, in two halves. The first half is set in 1984 - the Terminator is tracking Sarah Connor, but a Predator has come to Los Angeles to hunt. He spots the commotion at Tech Noir and his interest is piqued, so he fires a spear at the Terminator... to no effect. This puzzles the Predator, as does its weird thermal signature, so he starts actively hunting it. Confused as to how it keeps shrugging off what should be lethal damage for a human and can seemingly see right through its traps and camouflage, the Predator continues its pursuit. The Terminator, being increasingly sidetracked by the Predator's attacks, re-prioritizes the Predator as a threat to its mission, and actively engages him - it turns into a knock-down drag-out brawl, but the Predator comes out on top. Satisfied, he claims the Terminator's endoskull, and leaves. I'd have to make some kind of contrivance for why the Predator can't use the shoulder cannon to just one-shot the Terminator, but maybe the Predator initially starts out hunting some other target who gets a lucky gunshot off that damages the shoulder cannon, I dunno.
Part two takes place years later, when the Predator returns to earth for another hunt.
In 2028, in fact. As in, post Judgment Day.
The Predator is a little confused as to what Earth is a nuclear hellscape, but doesn't get much time to think about it as Skynet detects his ship and shoots it down, leaving the Predator stranded in the ruins of LA. Now being beset on all sides by murderous robots and hostile Resistance fighters, the Predator has to use every trick up his sleeve to stay one step ahead of his pursuers and find a way off the planet. An interesting thought would be that Skynet might be very interested in the prospect of easy interstellar travel.
