Lightning Ball: Knockback up, Blinding/Cooldown reducer, Range up
Blaze: Speed up, Slowing up, Blaze Lifespan up
Shock: Damage up, Attack Rate up, Lifesteal
Utility: Power Pills Turbo, Speed Up, Piggy Bank/Solar Tree
(If you're feeling brave or think you're joining a match a little ways in, sub in Med-i-Can for either of the solar boosters.)
Your order can vary, but once you hit each of these levels, I'd recommend you have the following items purchased.
Start: Bank/Tree, Lightning Ball
Up to Level 8: Move Speed Up, Blaze, Blaze Speed up 1, Power Pills 1, Shock Damage 1
Up to Level 16: Lifesteal, Shock Damage 2, Shock Damge 3, Power Pills 2, Power Pills 3
Up to Level 20: Attack Rate Up 1, Attack Rate Up 2, Blaze Speed up 2
Moving Forward: If you're playing offensively or up against a team that tends to cluster up (or a particularily turtley Voltar) get the Lightning Ball upgrades first. If you're on defense or against enemies that tend to scatter (or a particularily frustrating Leon) get the Blaze upgrades first.
Other Notes: If you're against a Voltar with a drone-oriented build, or a Yuri who spends 100% of the match fifty feet in the air dropping bombs, you may want to invest in Ball Range somewhere in the middle to eliminate Voltar's drones, or Knockback Up to take Yuri farther out of the air and leave either more defenseless.
Play Style and Tips
The biggest draw from this build is utilizing shock to the fullest potential; with full melee Coco can tear through droids, turrets and solar bosses without relying on burst damage's cooldown, and regain health while doing so, allowing her to stay on the field longer in doing so. In my experience, a lot of players tend to expect a Coco to be throwing 67-damage balls everywhere and otherwise being soft as a space kitten; this build greatly punishes players who think they can out-direct damage her.
Getting attack power (and max health of course, being on the frontlines much of the time) up is the biggest priority, as tearing through droids faster gets you more solar and eventually starts giving you health back (every pair of 50 health droids is a 24 health boost for Coco!) Damage up is a slightly higher DPS-to-Cost upgrade than attack speed, so you generally want to focus on that first. Make sure you're always killing droids and creeps. By the time you get to full damage and lifesteal you should be able to melt droids and get back any lost health from the encounter without having to do any acrobatics to avoid getting hit. Your turret destructibility is much better than a Lightning-Ball-Build Coco's is too, and you should take advantage of that either at any opening or even at full health to eat away at one. A couple of enemy droids moving toward you while attacking a turret can even provide a slight boost to your health as you go.
Her other moves are basically utility to her shock attack. Early game, Lightning Ball is Coco's greatest source of damage, but by the end of this build you'll use it to disorient and draw out opponents in order to quickly siphon out thier health instead of dealing 27 more damage every 5 seconds. Try to land the ball behind (and even slightly below) opponents. With the knockback, you can easily throw them a huge distance from thier starting points. For me it's a toss-up between cooldown and blinding; you can really disorient someone who's just been thrown by blinding them, but having the ability to remove opponents faster is important, too. Blaze's utility is of course in both catching fleeing Nauts and fleeing in a dangerous situation yourself; by endbuild a super-slowing trail of Blaze that lasts much longer than normal will keep persuers off and subdue targets.
Keep your eyes on the minimap, and try to engage any enemies against allies as quickly as possible. An enemy in the middle of a scuffle with another opponent will likely have consumed thier skills temporarily, and coming in with a blaze from the other side is a powerful trap. When going up against enemy nauts, attack quickly and unpredictably; make short hops to keep slow oppoents from getting away and targeting you, use Blaze right when high-jumpers attempt to flee to tangle them up and keep them with you. At full damage and health, you should be capable of soloing most Nauts; catch trap/explode Clunks unaware by coming right at them and piling on damage while they stick next to you hoping to blow you up; with both of his skills expended and you still getting health back, he'll be helpless. Any slower opponent, such as Lonestar, Rae or moving Derpl you should be able to keep up with even while meleeing. You jump slightly faster than Skolldir's double jump (with speedup), so just make sure you're in the air when that third fist starts to fly in. An enemy with a Voltar nearby is very defeatable; use lightning ball to remove as many of the drones as you can first (or with knockback, attempt to split the target from the healer) and Voltar becomes nothing more than another target to lifesiphon. With full damage and lifesteal you can also tear fown Gnaw's weedlings without suffering much.
Watch out for high DPSers like Dual-shot Froggy and Leon; it becomes a bit of an aim fight and you have to be wary when you aren't going to make it, even when leveraging your lower DPS with getting health back. Watch out for groups of burst-damage opponents when diving into a group of Nauts and droids; you can quickly wreak havoc on multiple targets and get more health back doing so, but watch for getting blown away all at once. Make sure you have Blaze for getting away in all the situations, instead of using it as part of your attack.
Sorona and Ribbit IV both greatly benefit this build; On Sorona Coco has tons of room to move around in the main area and can easily farm the solar bonus over the worm. On Ribbit IV there are tons of narrow tunnels underneath that make it easier to keep on aerial Nauts running scared, and the Solar Boss becomes incredibly farmable by level 10 or so. On AI Station this build suffers a little as there's a lot of vertical movement spaces and the gravity area isn't very good to Coco on the whole, making it harder for her to get to the neutral creeps and keep on opponents. Since there's basically one lane the whole way, it's harder for her to isolate droids to get health and solar.