You need 5 dark side ships at 4 star to unlock 5 star Executrix. You need 5 star Executrix, and 8 other 5 star ships to attempt the zeta challenge.
I have 4 DS ships at 4 star or better, Slave one is at 76/80....
And 7 ships at 5 star... Working on Sun Fac's ship at 10/65 currently.... I would be faster if to get plo koon's ship to 5 star, but I think I will need Sun Fac's ship at 5 star to get 5 star Executrix.
The fastest way to get one zeta equipped toon would be to use all your ship tokens on zetas, if your not buying ship packs you looking at months to create a fleet. IT does cost 40k ship tokens for 20 zetas... for that you could get 500 char shards, or 500(?) gear items... YOu could max out one of your chars for what it takes to give one a zeta ability.