These are the ranks you need to achieve to unlock each skin.

Skin	How to unlock
Alien - Nethead	Achieve Rank 34
Alien - Praetorian	Achieve Rank 19
Alien - Ridged	Achieve Rank 10
Alien - Warrior Dome	Achieve Rank 04
Marine - Connor	Achieve Rank 05
Marine - Gibson	Achieve Rank 02
Marine - Johnson	Achieve Rank 22
Marine - Moss	Achieve Rank 13
Marine - Rookie	Achieve Rank 28
Predator - Claw	Achieve Rank 03
Predator - Hunter	Achieve Rank 16
Predator - Spartan	Achieve Rank 31
Predator - Stalker	Achieve Rank 07
Predator - Wolf	Achieve Rank 25