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First shiny was a tentacool on the way to e4 in sapphire. It died.
Second was a bidoof in diamond, I had no pokeballs
Third was a riolu in black 2. I had just started and only had tepig and a lilipup. I had a bunch of pokeballs and began whittling its hp down after about 5 attempts with pokeball. Bout one third hp and it uses endure. Lilipups tackle lands a crit and leaves riolu with 1 hp. Catch it with premier ball and had the biggest smile on my face the rest of the day.