Base Attack Bonus: +10.
Race: Saiyan, Half-Saiyan, or Saiyan blood.
Skills: Concentration 13 ranks, Jump 13 ranks, Tumble 13 ranks.
Feats: Blink Rush
Special: Must have a Ki pool of at least 11 points, must have Unleashed Fury class feature
Other than what Garryl pointed out, looks good. I'd argue against a high stat requirement though, you shouldn't punish people for not having amazing stats for whatever reason. +10 BAB is enough to say you're one of the very strongest saiyans IMO. I do like the fluff requirement though, looks fun!
Z-fighter Abilities: Levels in Super Saiyan stack with levels in Z-Fighter for purposes of Ki abilities, unarmed damage, and unarmored speed.
Ki abilities, you mean the maximum ki surge he can store, or is he getting additional ki strike/blasts? Either way, must be more specific.
Kaioken Transformation: A super saiyan begins learning more powerful ways to unleash his fury, beginning with the Kaioken. The first time initiating the kaioken requires a full round action that provokes attacks of opportunity, but thereafter, uses the same action as activating Unleashed Fury. Once activated, the kaioken adds an additional 4 ki to the Unleash Fury ability, resulting in a more powerful fury. This ki is not actually a part of the super saiyan's ki pool, and only exists as long as the kaioken transformation lasts. A super saiyan may use this ability 3+Con mod times per day, and after it wears off, he becomes exhausted.
The 4 additional ki goes above his usual cap of half his class level or 4 additional ki for spending on his fury? Must specify. From what I read later in the class I assume the latter.
Ascension: The potential of the super saiyan form is fully realized as the super saiyan ascends. His unleash fury is augmented with 12 ki points, otherwise being identical to the previous forms. Further, he is surrounded by harmless electrical bursts, and his hair is even more spiked and longer skyward. Unlike the previous three transformations, Ascended Saiyan takes 2 full rounds to initiate the first time, but is otherwise identical in manifestation thereafter.
As in, he has 12 free points to spend on unleashed fury each time?
Looking it over, it looks good, but needs word clarification. As Garryl pointed out, prestige classes are meant to be relatively balanced with base classes, and should focus on making some aspect stronger at the expense of another aspect aka specializing. WOTC has infamously screwed up their own policy with some classes (wizard/sorcerer/cleric and their PrC's) but on the other hand many of the PrC's worked out well (Rogue and Assassin is a great example, many non-spellcasting PrC's too). Pathfinder does a GREAT job rebalancing base classes and prestige classes.
Also a quote from Welknair that is always helpful:
What's the first rule of homebrewing and creating additional material? "If you can't imagine someone not wanting to use it, it's too powerful. If you can't imagine someone wanting too use it, it's not powerful enough".
Anyway, the class looks on the whole great, and seems focused on buffing Unleashed Fury. I think that's a good idea. If you don't give them new ki strikes / blasts or the base class' capstone ability I think it's a good balance, trading some versatility for buffing one specific ability. Could even allow it more wiggle room for additional unique abilities.
I also like the idea of a blaster-focused PrC. Would be fun.