In less than 100 tries.
I caught a nearly perfect Timid Tapu Koko in Pokemon Sun after seventy-eight tries. This Pokemon has the following IVs:
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HP: 31
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Attack: 26
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Defense: 28
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Special Attack: 31
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Special Defense: 31
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Speed: 31
The Timid Nature boosts a Pokemon's Speed stat by 10 percent, while reducing its Attack stat by 10 percent. Since I won't be teaching this Pokemon a physical move, that stat doesn't matter.
If you evaluate the stats that matter, this Pokemon is just missing 3 IVs in its Defense. I can maximize that stat with Hyper Training, but just in case that option is axed in future Pokemon titles, my Pokemon will be future-proof.