Ok lets cross them off:
Predator 1: Hunter killed all the commandos and military guys, didnt kill anna. Hence doesnt kill non armed prey aka no sport and dishonourable (if you go by the books/comics).
Predator 2: Killed gangsters, cops, and the civilians on the train scene, but didnt realize they were civilians and not military or gangsters. Didnt kill the females in the film, which included the female cop and the drug lords concubine.
AVP: Killed mercenaries, Weyland, other guys, aliens all armed. Aliens and Weyland are an exception because the Alien is in effect is a weapon all in itself, and is a key part of the manhood or blooding ritual. Weyland because he was shown to have cancer and left alone, but when he provoked the predator, he killed Weyland because he was considered reasonable prey.
AVPR: In this film, he is a 'cleaner' and is on a mission to clean up the evidence of the predator technology and the alien infestation, therefore he is on a mission, not a hunt so he can disregard the rules in the name of completing the mission.