Short and sweet style.

Parrrley + Sheen = free bonus damage.

This build gives you plenty of damage output, plenty of mana to stay away from base, 87% crit chance (w/elixir 100%), 260% crit damage, and enough armor pen to piss off a tank. Your ulti gets a tiny boost on damage from the Tri-force, but the lower CD on it is all that really matters. Spam Parrrley and at try to attack everyone once, since your DoT from Scurvy will keep the 50% heal debuff on them for 10 seconds, hence why you don't need Ignite. Eat an orange if you are getting focused, hit Youmuu's if you have to escape or Ghost. And if anyone actually challenges you in melee, pop Youmuu's and crit their face off, they won't last long. Be cautious though, this build doesn't have any life steal, so you are relying on your oranges to save you there. You could replace the manamune with a bloodthirster if you really wanted to as well.

Armor pen = yay.
Bonus health is never a problem.
Lower CD always a plus.