There's a tab in your achievements for collectibles, that's where they go. The achievement registers as soon as you pick it up though so after that you can safely vendor or destroy it. Honestly they should just remove them at all as they're just confusing now - they're left over from times when in order for the achievement to register you needed to use it, consuming it in the process(they were also bound to account, not character, and thus bankable).

This achievement is one of the top 3 grinds in the game. Master Angler is the other one. The third one I will leave up to you.