well im glad you like it, and it is very difficult to complete, the insane cost is the only downside, usually better to use in 5v5s because they go longer, but it does work well in 3v3's too. Madreds bloodrazer is another option for your last item, especially against champions with really high health. also works great for soloing the baron while your team pushes the enemy's base. Feel free to edit it as you see fit, id'e be glad to hear whatever you come up with. Anyway, enjoy.

well you need two phantoms for a 100% crit chance, and they give lots of attack speed and dodge, and with two bloodthirsters you can hit 1k crits or more, and they give the most attack out of any weapon in the game besdies max sword of the occult stacks. also trinity force is a really well rounded item and bumps your crit chance up to 100% from 91, idk why everyone hates it so much. but if you dont like trinity force then three bloodthirsters is pretty beast, 500 base damage with 75% lifesteal, so you would heal about 800 health every hit, and would have somewhere around 1.1-1.3k health a second from lifesteal, and hit constant 1.2k crits. anyway, hope you like it

hearts are just for extra defence early on, you can get a heart and an avarice blade, or two avarice blades, but you'll probably die a lot early on without a heart.
thanks for pointing out the runes, i fixed it.
i didn't get boots because the items already give you a 42% bonus(30% from phantoms and 12% from trinity force)
also, trinity force brings your crit chance up to 100% and gives you a lot of other nice bonuses, like slow and bonus damage. without trinity force your crit chance is only 91%, and you loose all the other nice bonuses. but feel free to recommend a better item there if you want, I'm always open to suggestions. hope that helped explain some things

i choose the health because that way you have around 900 health at the start of the game with a ruby crystal, so you can fight the enemy longer. master yi already starts our with pretty decent dps, and rally and ignite make up for what he is lacking in items. of course you can easily get armor penetration or attack speed quints, its up to you. the build is pretty versatile, this is just a good base to start out with. the extra health does help quite a bit in the first few battles, which tends to have a big impact late game, but it is by no means necessary, hope you like it