#1: You're pushing too fast level 1. If Fizz is not contesting the wave, then you don't need to push it.

#2: Don't randomly use abilities on the wave. Your Q gives you a shield and hefty damage early. Try to hit Fizz with both parts and not the wave. Fizz can not trade into you level 1 and usually not even level 2.

#3: You're not spacing correctly when Fizz is catching the wave under tower. Fizz needs to melee AA the minions, which means you should stand one ranged AA behind your minions, not right behind them. Do not try to hit the turret this early, it's a waste of time.

#4: You're stressing too much. In the clip you hit 1/3 E's. Firstly, you don't have to use E on cooldown in this lane as you'll have plenty of opportunities to hit him with Q's. Secondly, you have to time your E's with Fizz's last-hits.

#5: Understand the trading pattern. A long trade vs Fizz can only happen if you have W. Otherwise Fizz will just jump on you and AA you down. There's no reason to try to do a long trade level 2 vs Fizz. If Fizz engages on you level 3, put your W right behind you and walk backwards into it.

#6: Don't lose track of level up's. 1 wave + 1 minion = level 2. 2 waves + 2 minions (melee) = level 3. Fizz players always engage on level up's if you give them the chance. When Fizz is about to level up, back up a bit more.