1. Farm gold until you get your first item Abyssal scepter and buy boots before health
2. Spam with Q
3. Fizz will mostly engage you with E first so shield must be ready
4. When fizz engage you near your turret it will most likely to use his dash and E. The trick here is that wait for him to activate his E to a target position (because his invulnerability for seconds make the tower shot and your skill worthless).
5 .When his E lands on a position use that chance to attack him there.Use E then W.
6. When the Enemy is lvl6 and above. Try to dodge as possible his Shark.When you cant, activate your shield or zhonyas.his shark damage is no joke.likely his combo will be R-E-Q-W.So your plan should be Shield first (if you are not able to dodge his shark) try to stick with him so that your shield will be extended.Then Q-R-R.
7. You can use 2 ult in a 10 sec 1v1 use it wisely.Q-R- auto attack-R.
8. you need at least have attkspeed item so that your passive activate fast

Always attack a Fizz after he use E Playful/trickster for that is his mean of in/ out of situation.