The key in this build is the offense. Utilizing those key B.F. items, I have maximized his damage output. No reason for offense when you cant live to reach the person, which is why i took leviatahn. My strategy with leviatahn is to try to kill steal champion kills as much as you can until you reach around 10 stacks. So what if your team rages? they'll thank you for saving them later in the game.
I say use the rush B.F. sword strategy so you waste no time getting all that damage instead of the effects i.e. armor shred from black cleaver. As using the first B.F. to upgrade I recommend Infinity edge as all your skills have on-hits and will give you insane killing potential, then next black cleaver for its synergy with ruthless predator's 3 hit with on-hit effects, lastly blood thirster for the survivability and longer fight time.
I take the merc treads to really give you that invulnerability to cc with the synergy of merc treads and cleanse. If the game lasts long enough, phantom dancers will be the best choice as it offers attack speed, crit chance, and movement speed to catch up to anybody.