The first shiny I encountered was Red Gyarados, but the first proper shiny I encountered was a Metapod in Ilex Forest in Gold. At the time, I didn't know what shinies were and thought it was something to do with the "forest guardian" thing the shrine mentioned, for some reason. I was a dumb kid. Anyway, I knocked it out with an accidental critical hit. In retrospect, it was a Metapod and I probably didn't actually need to weaken it at all. Really dumb kid.
The second shiny I encountered was a Skarmory in Sapphire. I encountered it with, like, only one or two Great Balls, and nothing else. It broke free of those and I ended up having to flee. Really, really dumb kid.
The first proper shiny I actually caught was a Flaaffy in SoulSilver. I was really excited to finally have a shiny, but I already had an Ampharos on my team, so it didn't actually get used. I always meant to go back and train it, though. Maybe I'll actually have to go ahead and do for X and Y. Could be fun!