If the target creature is an illegal target as Kimahri's last ability tries to resolve, it won't resolve and none of its effects will happen. You won't put a counter on Kimahri, and Kimahri won't become a copy of anything.

If the copied creature has {X} in its mana cost, X is 0.

If the copied creature is a token, Kimahri copies the original characteristics of that token as stated by the effect that created the token, with the listed exceptions.

Kimahri copies exactly what was printed on the original creature, with the listed exceptions (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 any Auras or Equipment attached to it, or any non-copy effects that have changed its types, color, power and toughness, and so on.

If the copied creature is copying something else, then Kimahri becomes a copy of whatever that creature is copying, with the listed exceptions.