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.

"Smoke screen" blocks line of sight of Illusions, so they can't heal anyone. You can deny enemy heals for 5 sec, just with one skill. Right timing and "smoke" placement is key issues.

If you have the Focusing Lens legendary, Skye can be countered if you use a Front Line as your meat shield. That Skye has nowhere to teleport; landing all five shots on her will be more devastating than you think.

Press F. You will teleport away and Skye can't catch you.