Instant
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The first target creature copies exactly what was printed on the other target creature and nothing else (unless that creature is copying something else or is a token; see below). It doesn’t copy whether that creature is tapped or untapped, whether it has any counters on it or Auras and Equipment attached to it, or any non-copy effects that have changed its power, toughness, types, color, and so on.
If the copied creature is a token, the first target creature copies the original characteristics of that token as stated by the effect that created that token.
If the copied creature is copying something else, then the first target creature becomes a copy of whatever that creature copied.
Any non-copy effects that applied to the first target creature before it becomes a copy of another creature will continue to apply once it becomes a copy. The same is true of any counters that are on the first creature.
When the first target creature becomes a copy of the other target creature, it’s neither entering nor leaving the battlefield. Any enters-the-battlefield or leaves-the-battlefield abilities won’t trigger.
If the second target creature is an illegal target as Fleeting Reflection tries to resolve, the first target creature will still gain hexproof until end of turn, and you’ll still untap it if it was tapped.