Rammus

Ban Rammus if you want to play Yi, he's more threat compare to Jax in lower elo. If you got matched against a Rammus, try not to fight him until you have Bloodrazor and a teammate is around and ready to help you. But don't use your Q to start, you should AA twice then E and get that Double Strike on True Damage. Your Q should be use to dodge his E.

Jax

If you're Gold or above, just ban Jax. He counter Yi all the way after lv4 and you have no ways of dealing him if he got fed.

Shaco

You don't have to worry about him a lot, but still keep an eye on him if you ever got matched with one.

Volibear

Before you hit lv6, try not to fight Volibear since he have an OP passive as well as Q and E for CC. (Dont underestimate his damage even if he's just a tank)

Rengar

Invade his Jungle anytime, he can't do a lot of damage to you since you have your W and Q to dodge.

Kindred

This could goes very tricky, if you got matched against a good Kindred player, you could get kited by her very easily in early fight and she could still escape with her Q if she needs it.

Wukong

Same as rengar, Invade his jungle. (Also he's Master Yi's apprentice btw so don't worry too much )

Warwick

Lee Sin

Amumu

Kha'Zix

Trundle

Evelynn

Graves

Elise

Ivern

Xin Zhao

Pantheon

Hard to deal with early game. But you beat him after your Bloodrazor and Guinsoo.

Nocturne

Kayn

Lulu

Avoid going in first in team fight because you can't do anything after she use her W on you.

Malphite

Malzahar

Udyr

Vayne