Traits are the Power and Weapon sets that you possess. Your Traits can be reset by visiting a terminal at one of these locations:
Hero: Southwest corner of the Watchtower, known as the Aquacultural Area.
Villain: The Pit section of the Hall of Doom. (Map location is not known.)
It costs a flat fee of $500 to re-spec your traits. If you re-spec several time in the same 24 hour window, the cost will increase every time. Once 24 hours have passed since your last re-spec, the cost will go down to the original $500 cost.