Drogoz is a good counter since he flies and inaras projectiles are hard to hit and specially if you have W.Y.R.M Jets.If you are good at aiming then the direct shot damage bonus may even be better.
Your weapon attacks are very precise and deal a surprisingly large amount of damage. Barring if he's being healed, if you focus your attacks on Drogoz, you should be able to take him down within a single clip.
Never, NEVER ult first. Save it for when he innevitably grabs you and tosses you off the map. When he does, spam your ult button - it will stop your momentum the moment he lets go, and bring you back to safety.
When you are outside of stealth detection range but within the Retribution range, the insignia will still appear above Skye even though she is invisible. Shoot below it for expected results.
To avoid a Drogoz ult, find a corner and wall yourself as close as possible without "jumping on top" of your wall. This will prevent the Drogoz from reaching you.