Okay, I'm assuming that you were laning against the Fizz in this game: http://matchhistory.na.leagueoflegends.com/en/#match-history/NA1/200777819
Well, looking at your build path, you bought early magic resistance, which is good. However, I would suggest you don't rush Mercury Treads as the mobility doesn't really help as much against Fizz early as you may hope. You also started cloth armor, which might not be the best option.
When laning against Fizz, you want to harass him a lot early to build a lead and survive his early all-in attempts. To this end as Gnar, I would suggest starting Long Sword and building an early Hexdrinker. You want to poke and harass him down while avoiding all-ins against Fizz, especially when he has ignite and you have teleport.
I notice that you died around 3:23 to the Fizz in lane, which started his snowball. Fizz has high all-in potential in the early levels (1-3), so you have to be careful not to allow him the chance. I would recommend taking E instead of W at level 2 so that you can escape if her tries to fight you and then proceed to kite him while his abilities are on cooldown. Also, push the lane early and ward when possible to get an early level 2; hitting level 2 before your opponent can allow you to get a cheese kill on them or give you an advantage. Push Fizz under the tower and harass him for every CS he takes.
You have another advantage due to Gnar's status as a manaless champion. Fizz's E costs a lot of mana so you can easily run him OOM if he has to use it repeatedly. You have free ranged poke, so use it when you can.
Misc Tips for Gnar.
Consider taking Oppression in the defensive tree because of Gnar's CC and slows. It reduces quite a bit of damage.
Against squishy opponents, you might want to max E second for the reduced CD and increased damage.