@CaffeiNix: My guess is it's too obvious and powerful. Kind of like why telepaths can't simply turn people's brains off or make them seize out. It wouldn't even be a fight. If a telekinetic can lift hundreds of lbs then surely pulverizing someone's soft & squishy vital organs is simple stuff.
That's what I'd do anyway. Heaven help the world if I ever get psychic powers.
Thanos (no IG) wins against Green Phoenix. Dark Phoenix wins (no IG). Thanos (with IG) beats Dark Phoenix White Phoenix wins IG or not. She's an omniversal powerhouse, yes? According to wiki, IG only works in the universe it's from. White Phoenix could probably drag Thanos to another universe or the White Hot Room where the IG may not work. She may even be strong enough to just screw with them directly the way TLT did.
A big question is whether the cloak of invisibility masks heat signatures. Considering that it's one of the deathly hallows and can even hide the user from Death itself, I'm just going to assume that Predator can't find Harry either. Since the Predator's cloaking is light bending based, Harry could probably cast luminos to reveal the Predator. Also, the Marauder's Map!
Really, the Predator's best shot at winning was to take them out immediately. Giving them time to catch their breath isn't good. They have too many weapons/spells at their disposal + knowledge of Hogwarts. They could slink away to the Room of Requirement or Gryffindor commons to work out a plan where the Predator can't reach them.