I've lately started playing alot of Shyvana Jungle and have yet to lose to any Yi, though having played vs loads of them in the last few days.
Advice 1.
As Shyvana: Build devourer as usual, but instead of going after Bork directly after, go deadmans instead and spirit visage after that. Why you might ask? The deadmans is probably obvious, as it will shave off alot of his physical dmg, however, as Yi will also be going devourer, and guinsoo he will be doing a metric ton of magic damage as well. I've done this build path every game and haven't failed yet to duel any Yi. You won't do exacly as much dmg as him, but while he will be squishy, you will be tanky as hell and aslo dealing massive magic damage.
Note: This is just for the one vs one scenario.
Advice 2.
Might be worth cautioning your teammates to play very safe early and not push lane, Yi might lack cc but makes up alot of it with his rapid kill potential, much like Rengar, if he doesn't get fed, he'll be having a hard time scaling up fast enough, some good Yi's will circumvent this by farming the jungle hard, depending on how he plays, use it to your favor. If he ganks alot early, he won't be farming alot, if he farms alot, means you got a prime opportunity to set your team ahead of his.
As he is so squishy early, you can actually invade him and kill him if you got decent map awareness.
Advice 3.
Masteries and runes! Make sure they are optimal!
Personally, as Shyvana has among the strongest jungle clear in the game. I generally focus my masteries around her scaling, going full AS reds, armor yellows, 6x cdr per level blues, 3x mres.per lvl blues and cdr per level quints. Doesn't give you the best early game presence, but if you time your ganks well that won't matter, Shyvana's effectiveness is dependant on cdr while not having very little room to get cdr items that's why I think this is pretty optimal.
As for masteries, my preferred favorit is:
18 ferocity, go piercing thoughts instead of battering blows as you will be doing more magic damage than physical between ur devourer, w, and e.
12 resolve, go defensive over sustaining, if you take a rift scuttler between each clears you will never lack health as you get loads back by taking the scuttler, I generally full clear, take a scuttler, then gank with full hp.
Advice 4.
As shyvana is really good at clearing and sustaining in the jungle, use this to time your backs for optimal buys, I generally back when I have enough gold to get a stalkers blade and dagger and a pot or two, my next back tends to be when I can buy devourer and boots, that timing has worked excellent for me. Always go stalkers blade as Shyvana, it gives you extra utility, that is peeling and chasing potential, if you use it well you won't need BotrK to score kills, don't ever take skirmish saber unless you are VERY confident with your Shyvana game or intend to rush bork after devourer, why? Because you already deal a metric ton of damage and are among the best duelers/skirmishers in the game, even without the damage boost, you don't actually need it, but I can see advanced Shyv players making good use of it.
Advice 5.
Last but not least, don't fool around, close the game as soon as you get a chance, don't take chances to farm kills. Yi is a beast once he is fully built.
Don't let him get there.
Hope this helps you improve your Shyv game, good luck and happy hunting.