I've only desynthed as far as Mahi mahi but I've gotten only shards & crystals so far no clusters.
The fish I broke down have so far given me water,earth and fire shards so I get the feeling depending what/where you fish you can pretty much get every type of shard though the most I've gotten is up to 3 from 1 fish.

I think the best thing to come out of the fish are the clear demimateria II as it sells to NPC for 1000 gil.

Culinarian is up to 68ish so I'll be fishing up some more mahis this week to level him up (its going at snail speed now ><) so I can finally get started on breaking down my 2 star fish collection