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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