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Lawful Good is Lt. Gorman, representing the general command of the marines. Command often does things by the book, but can do or order things that seem stupid because they stick to a code and disregard other people in pursuit of the win.
Neutral Good is the Colonial Marines themselves, representing the general good. They want to kill the aliens and restore peace, generally, in any way possible.
Chaotic Good is Pvt. Hudson, representing the boots on the ground. The standards unga dunga, they riot for attachments and display a general dislike for anyone higher in rank than them, but they also want to wipe out the aliens as much as everyone else.
Lawful Netural is, of course, the Predators. They kill as part of their society, and follow a code in doing so yet they truly fight for no side on the planet.
True Neutral is the zombies. They represent an animalistic force that has no sides, targeting all equally.
Chaotic Neutral is the bad blood. They disregard the rules of the Predators for their own personal gain, yet still stick to their own side and do good or evil as it pleases them.
Lawful Evil is the classic Xenomorphs. They are a hivemind, the natural extension of law and order, focusing entirely on the hive's personal gain in the form of hosts.
Neutral Evil is Weyland-Yutani. They are willing to use anything from the law of the Marines or their own scientists to gain money.
Chaotic Evil is, lastly, the corrupted Xeno. They are here because there was nothing else to put there because they represent the defiance of the "true" Queen. As a result, nobody likes them that much.