Actually Kayle is a big counter to Fizz and all other assassins. He has good poke damage, and can heal himself and if Fizz tries to all in him, he can ult. He has a super slow laning phase, and doesn't start to get beefy till mid to late game. But if you are behind its hard to catch up, just farm as much as you can and then you'll get your strength. Guinsoo's Rageblade and Nashor's Tooth is his core.
Notice he can probably win against most of these champions if he outplays you, so you need to know what the counter is about and play accordingly. Also some are hardest counters than others (I ordered the general counters in order from hardest counter to mildest counter) and some might not be counters depending on both champions' builds.
As a general tool you can use in these cases: http://www.lolcounter.com/champions/fizz
Some champions have bad recommendations (it's popular vote) but you can check the comments on matchups so you kinda have some feedback going around sometimes, mostly in the form of "how to play this matchup".
Notice he can probably win against most of these champions if he outplays you, so you need to know what the counter is about and play accordingly. Also some are hardest counters than others (I ordered the general counters in order from hardest counter to mildest counter) and some might not be counters depending on both champions' builds.
As a general tool you can use in these cases: http://www.lolcounter.com/champions/fizz
Some champions have bad recommendations (it's popular vote) but you can check the comments on matchups so you kinda have some feedback going around sometimes, mostly in the form of "how to play this matchup".