Given this rarity and mythical status, the information stated about them (and on this page) may be subject to hyperbole or distortion from being passed down through the centuries. Scott's statement of "I'm a true Alpha. You have no idea what I can do." in 3x17 - Silverfinger is a subtle bit of lampshading to this point as neither the Twins, Scott, nor the audience truly know what a True Alpha can do. That said, here are a few more points of what we have been told or have observed:
A werewolf cannot attain True Alpha status if they ever kill someone.
A True Alpha's power can only be taken by a beta turned by their own bite.
In Lunar Ellipse, Scott rises the alpha rank by determinedly pushing through a mountain ash barrier, successfully breaking it, fully awakening his True Alpha power.