The thing about Shaco is that he is high damage, but incredibly squishy. If you survive his initial burst, there's a good chance you can kill him. Shaco needs to snowball early to be relevant. If you shut him down early, it is incredibly difficult for him to get back into the game. If Shaco ganks and gets nothing from it, it's a huge problem. Counterganking is probably one of the most effective ways to shut down a Shaco. You need to have a good sense of where he is for that, which brings me to my next point.

The main thing I would recommend is to invest in wards. Defensive wards will shut Shaco down pretty hard, since he needs the element of surprise to do his thing. 400 gold worth of stealth wards will not set you too far back, and might give you some game changing vision. A pink ward either behind your red buff near river entrance, or in the bush next to the river between your blue buff and the river. See if you can convince the support to pink the tribush too.

For 1v1 fights, invest in an upgraded red sweeper as soon as possible: it gives you ten seconds of true sight like a raptor buff and lets you see any stealthed champions as you move around, not just in the area you sweep.

Lots of people argue that Lee Sin counters Shaco, but I would argue that he only counters him 1-6. After that, it's a skill matchup. Same thing with Rek Sai. Nunu does very well against Shaco, his high hp will help you survive his burst and Shaco boxes will only heal you. Nunu is quite strong in jungle just in general. Twisted Fate is a soft counter.

Oh one more thing: try not to turn your back on him when he AAs or Es, it gives him %20 extra damage.