To get a predator core, you must defeat one of 33 Predator Pals around the map. Predator Pals are similar to field bosses, except they don't appear on your map and they aren't catchable.
However, predator cores can be pretty hard to come by as you'll need to find rampaging Predator Pals across the map. Predator Pals do respawn, but they don't seem to have a 100% spawn rate.
We've found that fast traveling to one of the nearby waypoints and refreshing the area by returning to the main menu has assisted with the spawn rates.
Keep in mind, Predator Pals do not seem to have a 100% spawn rate, so there is a chance that you arrive at one of the marked locations and there is nothing there.
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