Yeah, Parnell requires more precision than the other Assaults. His SS, when it works, is his best tool. I run Capacity Increase by the way - really helps his Super Solider.
If he can stay in the Monster’s face, the Monster will almost always run. As a Monster, if I have full/a lot of armor, and Hyde or Markov have their main weapon on me, I don’t always feel the pressure to disengage. They melt the armor too slowly. If I’m up against Parnell, I focus the Trapper and I see Parnell running over with that red glow on him, I will absolutely disengage. He will demolish the Monster’s armor way too quickly.
Also pop SS right when you engage in the dome - this will take most of the Monster’s armor. Don’t use your SS right away when it’s recharged - consider chipping his armor away slowly and as soon as it is about run out then you pop SS and it will do a ton of permanent health damage. Then once the dome is out, stay on him with the Rocket Launcher, it doesn’t do great damage but it does great chip damage. The blast radius of each round is pretty significant.
In short, his burst is insane, and you can even save your teammate because they all fear the rage trooper!