The kineticist from Occult Adventures easily fits the bill for a Dragon Ball class. They even start with an ability to "power up" and throw energy blasts at-will.
I recommend that because designing classes is really difficult, even for professional game designers that create RPG content for a living.
Except for the part where, you know, Goku and company don't suddenly get easier to knock out the more attacks they fling.
And they're not locked into a single element. And don't even deal elemental damage at all.
The Kineticist does not really model any DBZ character well at all.
@The OP: The whole class feels very...clunky, to say the least. It breaks a general trend among PFRPG classes (HD and BaB are tied together, so d10 HD would tie with full BaB, though that's not such a bad thing), and the "Paths" are not very well fleshed out, nor do they really fit the archetypes of most DBZ characters (most characters tending to trend towards the "Lightning Brusiser" instead of being based on strength/speed/intelligence to the exclusion of other things).
I'd take a more critical eye while watching next time you view an episode, and look at how every character fights. If you want there to be paths for each member of the class to choose between, focus on those.
For example, Vegeta is very much a furious, rage based fighter, while Piccolo stays calm and collected through every fight he's ever in. Their techniques reflect this, with Vegeta tending towards huge blasts, punches of great speed and power with little finesse, and a love of big flashy finishing moves (Final Flash, Final Explosion, various other "Final" attacks).
Piccolo meanwhile trends towards attacks that focus on either outmaneuverig or tricking the enemy, such as his Hellzone Grenade (Multiple blasts fired to appear as if he missed...when in reality he was surrounding his opponent with blasts that were then impossible to dodge because of their position).
ikewise in their interpersonal interactions and in battle, Vegeta is short to his allies, and very brash and reckless, while Piccolo assumes a leadership role quite easily, and knows his own limits.
Make the Paths focus on those strengths. A "Fury" path that gives raw power at the expense of defensive ability (Like rage, but perhaps not precisely Rage). That path would focus on being THE BEST THERE IS, while having little team based application.
Meanwhile, there is a "Focused" path based around keeping your head and utilizing tactical abilities, maybe having some synergy with Teamwork Feats, or a Bardic Performance-like ability to buff allies even when on the sidelines, or outsmart your enemies with tricky "Ricochet shots" and the like.
There are other potential paths based on the other main characters, but those are the easiest to visualize.
There're already a number of Classes which let you play Dragonball-style character.
Qinggong Monk gives you Ki and lets you use Ki to cast spells like Scorching Ray.
Bloodrager gets you the blasting, flying, etc., and Rages like going Super Saiyan.
Warpriest "Powers up" every round on the round by burning Ki. Sacred Fist ESPECIALLY is a Monk which "powers up" practically constantly. BOTH can perform a Kamehameha with Blood Crow Strike.
In all honesty, I can't think of a damn thing in Dragonball that can't be done (at least in theme, though not overall power), that can't be accomplished by simply playing a Sacred Fist/Bloodrager Gestalt or simply Multiclass.
Except for the part where, you know, Goku and company don't suddenly get easier to knock out the more attacks they fling.
And they're not locked into a single element. And don't even deal elemental damage at all.
The Kineticist does not really model any DBZ character well at all.
Energy attacks in Dragon Ball burn enemies and cause explosions. They'd be modeled as fire damage in Pathfinder or possibly electricity damage.
Energy attacks do fatigue characters in Dragon Ball. It lowers their power level and makes them more susceptible damage. There's many cases where a character fatigued themselves using an energy attack only for an enemy to beat them up because they lacked the stamina to resist. The Dragon Ball Collectible Card Game even has energy attacks drain your health.
I do think one thing hindering a dragon ball character with the kinectist is the lack of Improved Unarmed Strike unless you get that archetype that takes away ranged blasts.
Fatigue, yes.
Nonlethal, no.
And the fact that Ki is restored by eating Senzu Beans means it's definitely not Burn, which as written can't even be removed without rest if a deity wants to take it away.
Actually, you gave me an idea. One could make an archetype that replaces burn with another resource mechanic more befitting Dragon Ball ki.
I still suggest making it an archetype. Designing classes is one of the hardest things to do in this game. There's a lot of design overhead in making a class. You're better off just modifying an existing one, especially when you're borrowing abilities from other classes.
I would simply recommend UC Monk and just add custom abilities to the Ki power list to fill the gaps.
Edit: Try this, its not mine but its taken from an unchained discussion where people wanted a definite brawling monk and a mystic monk, what it seems you would want more, instead of UC being stuck in the middle.