Silver and Gold items all come from bosses. Silver are common drops from bosses, Gold are rare.
Hands down the best way to farm materials is Quiz levels, which involve you fighting specific enemies. This gives you complete control over which materials to farm. Simply select a Quiz level that has you fight enemies which drop materials you want and replay it as needed.
Now that you've picked a level, there are a few other things you can do to improve your chances of getting gold materials. Equipping a weapon with the materials skill improves your chances of getting better materials, as does using alchemy. Finally, in focused spirit mode (the mode that consumes magic power), racking up KOs (I believe every 25) will grant you bonuses (randomly selected until you get all of them at 150KOs), one of which is more rare materials dropped. Finally, the DLC maps (Twilight, I believe) allow enemies to drop two materials each.
Here's a list of where to farm the heroes and large bosses:
Link: Adventure map A-5
Impa: Adventure map A-5, B-2, or E-13 (all roughly equal IMO)
Sheik: Adventure map C-11, E-13
Zelda: Adventure map A-5, B-2, F-6 (slight edge to F-6)
Lana: Adventure map A-5, B-10, G-15 (slight edge to B-10)
Ganondorf: Adventure map A-5, A-15, B-2
Darunia: Adventure map B-2, B-13, E-13
Ruto: Adventure map A-15, B-13, E-13
Agitha: Adventure map A-15, B-2, F-6
Midna: Adventure map A-15, B-10, F-6
Zant: Adventure map B-2
Fi: Adventure map A-15, H-6
Ghirahim: Adventure map A-5, B-13, F-6, H-6
All of these levels are quiz levels. As a rule of thumb, keep the enemy onscreen as you defeat them or there is a chance they won't drop materials. I will continue to update this with more information.