Here are some thoughts on killing SCH in PvP. Since a healer is often the first target, and SCH can put up a formidable defense (as can WHM, but this is not a thread about whether SCH or WHM is better), it is good to know a couple tricks for dealing with a good SCH.
The best thing you can learn for taking out a SCH, is when the SCH pops attunement, switch immediately to killing Eos rather then waste your time or CD's on the SCH. This one tip will work wonders for you. In fact all of the tips in this thread revolve around this idea: know when to switch between the SCH and Eos.
I used to look down on people who said to kill Eos first, and while I still prefer to go for the SCH initially, it does make sense to switch to killing Eos when you start to have trouble killing the SCH.