Shaco One-Trick here.
Tryndamere and other % health duelists tend to completely wreck Shaco late game. While it's very difficult to do anything about him getting away, your presence in a lane can be enough to deter him from hanging around for too long.
Duelists like Jax, Fiora, Tryn and especially high DPS tanks like Singed are often very good picks against him. You can hold the lane vs him and he can't really fight you late game unless he's either way ahead or significantly outplays you.
What Shaco really lacks is the capacity to one shot people anymore. A Caitlyn beneath a tower is still very difficult to get at for Shaco unless he ulties. And anyone a bit tankier will probably just kill him if he tries to dive. He's also succeptible to counter waveclear, since his dives are fairly weak, he relies heavily on a minion wave to push in and get him under tower. If he Q's to get under tower, he loses a valuable asset. How a Shaco uses his Q is the difference between the good and bad clowns.
Anyone with waveclear can hold a tower against a splitpushing Shaco provided that he's not fed as hell, by denying him from pushing in his wave.
A problem happens when you send one of your carries over to deal with him. Since Shaco relies a lot on being separated from his team in order to pull pressure away from the rest of the map, 2 or 3 people who roam into a lane in order to try to catch the Shaco more often than not only ends up in even more of a disadvantage.
For one, you probably won't catch a good Shaco anyways, even if you have the element of surprise and sending any more than 1 person to deal with him can cripple your map pressure and let his team steamroll objectives.
The longer a Shaco hugs a lane, the more he's trying to goad your team into a chase. The technical term for a long-term Shaco chase is, in fact, a Clown Fiesta. And he'll run you all over the jungle with his BM's and boxes.
The safest bet to deal with a split pushing Shaco is to post one person who can't die to a tower dive from him and who can waveclear pretty well. A Tryndamere with a Shiv can do these things quite well. Shaco can't burst you down as Trynd and you have enough damage to kill him in your ulti if he tries. I instaban Tryndamere every time as Shaco, because if he gets fed, he's nearly impossible to deal with for the clown.
The most important lesson to learn with Shaco, though? Don't bother chasing him. You will waste so much time trying to catch him that even if you do manage to, it'll rarely be worth it.
