The ones that drop from monsters are for achievements and dyes. The ones that are dungeon or quest rewards usually have some ability or display when you use. The ones for achievements, and for fish, should be captured by your account as soon as it is in inventory, so you are free to sell them thereafter. I do recommend you check you achievements first, as a few are bugged and not counting to the achievement yet. As for the non-achievement trophies, it is up to you. There are quite a few in the game, so keeping them does impact storage. IIRC, these can only be destroyed, not sold.