I believe, once you enter Hyrule Castle once, a silver one starts appearing around the map? It, along with a few other silver monster counterparts, will drop rare gems and other once defeated. They also have increased HP and are quite the challenge to defeat, especially if you aren't prepared. Silver monsters are often distinguished by the whiteish colour (In a Lynel's case, mane) of which is accompanied by purple stripes.
Just yesterday I saw the silver one for the first time. So that's actually four tiers. I've never been in Hyrule Castle, though, so I think monster difficulty is tied to divine beast/shrine progress.
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Also the defense on it is so grotesquely high that I don't take much damage from anything in general. Now I'm working on the Radiant set (just because it looks cool even though it really sucks as actual armor rip) and the Champion's Tunic (only need Dinraal's horn!). I have 85 Koroks and am mostly focusing on weapon slot upgrades, but I think I'm going to focus more on bows after my next upgrade.