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, given they have the potential to do so, gradually attains the status of True Alpha but if they kill someone, they destroy that potential.
A True Alpha's power can only be taken by a beta created by their own bite.
In the movie, Derek Hale sacrifices himself to destroy the nogitsune and save the people he loved including his son, by restraining the dark kitsune and allowing Parrish to incinerate them both in hellfire. In the blaze, Derek's blue eyes changed to alpha red, becoming an alpha as a result of his brave sacrifice just before his apparent death. It has not been confirmed if this makes Derek a True Alpha or if there is a different explanation. In particular, this would poke holes in the assumption that killing someone prevents a werewolf from becoming a True Alpha. Other potential reasons could include an evolution such as when Derek attained the full shift/wolf transformation or if the sacrifice reignited his dormant alpha spark that he previously sacrificed to save Cora.