Use the noob Combo, Plasma Pistol + Battle Rifle.
Use the Plasma Pistol to take down Elite shields, the BR to headshot them
If you need more help PM me, I can link you to Walkthrough Vids.
that isnt the noob combo the noob combo is where you have plasma pistol/smg or human pistol or plasma rifle things dual weild able hince the name noob COMBO
A combo doesn't have to be a d/w Combo, there is a gametype devised by Bungie for the TAS playlist called "Combo Training", it features the PP and the BR.
The Pro combo btw is the SR & BR