(Assuming you're talking about the first Arbiter mission)
Not panicking mid battle would be a good start. Rather than spraying everywhere, try to focus your shots.
Secondly, use the Carbine and/or Energy Sword. Use them to take out the holo-drones.
Lastly, you are not required to kill him in one fell swoop. If your shields are low/down, pull back and let them recover before renewing the assault.
Also, try nades. They always work wonders, especially if you stick someone.

If that's the case, an energy sword will make life a lot easier. Assuming that you picked up a beam rifle previously, eliminate one of the honor guards and grab their sword. Rush through til you get to the Prophet, and then jump on his throne and board him. Use grenades (frag AND plasma) where needed.
At least, that's how I did it.