When playing as a melee champion, do not go for extended trades with Fizz as he will always come out ahead thanks to his W.
Unless you benefit from any other wave manipulation, try and keep the wave even or closer to your side. This prevents him from engaging on you or chasing you down.
Fizz has insane roaming potential. Do not blindly follow him as he can easily turn around and kill you. Instead, communicate with your team while following him from a distance if possible.
When walking around Summoners Rift, do not go alone if you’re squishy. Fizz can easily assassinate somebody who is walking through the river alone. Take appropriate paths through warded areas whenever possible.
Do not use any executing abilities or key skill shots on Fizz unless he has used his E as he can easily dodge them by going untargetable.
If you’re hit by Fizz’s Ultimate R, do not walk close to your allies as the AOE damage from his shark will deal lots of damage to them too. Walk towards them but don’t get close.
Fizz has good kill pressure at level 3 and 4. Respect his all-in and try to poke him down before he gets the chance to play aggressive.
Fizz's Playful / Trickster E allows him to dodge damage and escape from trades. Do not go for all-ins unless he has already used this ability beforehand so you’re guaranteed to hit your abilities on him.
Keep an eye on your XP bar between levels 5 and 6. If you think Fizz is going to hit level 6 first, try to stay at max distance and play safer. When Fizz hits level 6, his kill pressure intensifies and he can easily kill you if you’re level 5 and are overextended.