If I use Sylveon's "Wink Wink" attack to have my opponent discard Ilima, can I use Victini's "Victory Star" Ability to force my opponent to re-flip their coins?

Yes, you can. If your opponent flips a coin as part of your Pokemon's attack, you can use "Victory Star" to force them to re-flip those coins; but keep in mind you will have to re-flip your coins for Ilima too.

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