There are 5 types of transformations:
Each Transformation has 4 growth stages. Which rank up by adding the special skill points you earn from leveling, unlike AP, these are 10 points for your transformation skills. Example:
Falcon-->Falcon justice-->Falcon wave-->Falcon Sage
Savage Beast-->Beast Slugger-->Iron Beast-->Beast Lord
Paladin-->White Knight-->Holy Knight-->Champion
Dark Knight-->Black Knight-->Chaos Knight-->Infra Black
To "rank up" your transformation, you DON'T need AP (Ability Points).
You just need to level and it will rank up after an amount of time.
Transformations are attained upon completion of Generation 2, for all races. (As of G16S2)
Dark knight is available after G3 Mainstream Quest.
Paladin and Dark knight are only available to Humans.
Awakening of Light (A.K.A. Demigod) becomes available after completion of the Generation 10 Mainstream.