Purple Stars

You have to have a character level 85, have 20 zeta materials (which can be obtained through the last tier of the ship ability mats daily challenge, through grand arena/territory war as well as events), and a certain amount of omega materials ranging from 10-18 (I believe.) These can be obtained through Omega challenges, completing daily task list, grand arena, ability, ability mats daily challenge etc. Furthermore you will need at least 20 mk3 purple ability mats, and the character in question must first have a zeta ability able to be applied (not every character has one) as well as have the ability in question maxed to its highest tier (excluding the zeta tier.)