I've played yi for a year i've got about 470k mastery on master yi. i've tested lots of different builds on yi and have great knowledge of the champ.

Presision
Although i prefer lethal tempo, Conqueror is considered better and does more damage in later stages of the game.
Triumph is pretty self explanatory.
legend: tenacity Is my preferred runes over attack speed and life steal. considering most champ in the game have some sort of cc, legend: Tenacity Combined with Mercury Treads can half the stun length of all stuns, roots and silences.
Coup De Grace is the better option then the other two.

Inspiration
Magical footwear save you gold and won't delay your essence reaver rush.
Gosmic insight gives cdr and cdr is op.

Core
Essense reaver rush is really good and decreases your q cdr by 20% each auto. it works much better with rageblade and let's you q every second with enough attack speed and cooldown reduction.
skirmishers sabre: bloodrazor is next because you need more attacks speed for your essence reaver passive. also its good for objectives e.g. drag, baron and crab.
Rageblade is insanely good (ty riot) and is core for essense reaver.

Ninja Tabi is good for heavy ad comps or if the enemy adc is fed.
Mercury Treads are great with your legend tenacity.

Situationals
Tanky items aren't required but can be very useful. enough said. tanks win games so why not get something.
lifesteal items, more tanky items, most items work after you have the core items. build banner of command if you like it probably works.

New Item - Spear of Shojin:
this item is really good and i will consider building it 5th or 6th. get this instead of a tanky item.