When fighting Fizz (and assassins in general), keep this in mind
Fizz can, and will, jump in and instagib you given the chance. With his burst, slipperiness, and mobility, he can get away with it.
However, this does not mean that he will constantly engage on you; good Fizz players recognize threats (CC, major targeted damage spells, you know)
No Fizz wants to be charmed under tower.
Fizz players will identify any ways you can turn an assassination, bait them out, and then kill you while you can't respond.
For example:
He puts himself in a position where the enemy 
can easily combo him. He dodges it with Q, and if burned his stun in the attempt, Fizz will go in for the kill.
He gets trapped in 
cage, but E's out. Since his E cooldown is shorter than the cage cooldown, he waits for the spell to come up and kills Veigar while he can't stun the fish, being careful to E Veigar ult.
Basically, If you are a champion who has a spell that can be used to completley shut down an assassination attempt, but is otherwise chum in the water, you HAVE to save that spell to save your ass if you don't want to be shark bait.
