I've desynthed over 1,000 fish, hit level 71 culinary desynth from it, here are some findings:

You'll get water shards, water+earth on dunefish, water+wind on skyfish
Level ~45+ fish will give crystals instead of shards
You will get crap demimateria, I've only seen clear
Fish are made out of sand, mostly fine sand, some silver/electrum/gold
You can also get pigments from fish, and some give lures
At 70 skill, you might get 0.03 skill from a 1 star fish