We have only actually seen the pred claim trophies from prey which he has killed in a close range fight. I know about the skull with the hole through it but maybe it could've been a skull from a previous hunt. In pred 1 Billy stood up to the predator with only a knife, he died a horrible death but the predator considered that an honourable & brave challenge from another warior so he took his skull. The same thing happened in ppred 2 with King Willie & Jerry, they both fought back in close range combat, the predator is seen taking both of their skulls. The predator, to me anyway, only sems to make trophies out of prey which put up an honourable fight & which have the guts to stand up to it, 1 on 1. There's hardly any honour in taking a trophy of prey which you just shot while they were unaware. As for the skinning & hanging, the preds use that as an indimidation tactic, to strike fear into the heart of their prey, it makes the hunt more interesting, it'd put the $#its up anything to see their own kind skinned & hanging upside down. It's is also used to show their hunting territory, to ward off rival hunters, letting them know that this is their preferred hunting ground.