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I only caught 2 shinies so far, both in Gen III.
My first shiny was a Poochyena in Sapphire. I never had a shiny that I actually caught on my own, so I decided to look for my favorite mon. Needless to say, it took me a while to find one.
A few weeks later, while looking for a Chimecho to trade to LeafGreen, I found a shiny Duskull which I traded to Gale of Darkness.