If Tyra is using the First Blood legendary card and/or liferip, you can use cauterize to counter the healing.

Keep an eye on your turrets. They may lock on to Skye while she is behind you. This will give you a big head's up.

Lower your music's volume and listen for sound effects. If you're her target, you might hear her coming. If you aren't, you might be able to save an ally.

As with all healers, start with poison bolts so her illusions can't heal her fully. She'll receive 1/2 the healing for 3 seconds.