Using the links here

http://www.myrevolutionarywar.com/index.htm

you can develop a list of what Continental Regiments were at this battle.

Then you can find all Campbells listed on the surviving rosters of these Regiments using the index to NARA Micropublication M246, "Revolutionary War Rolls" on ancestry.com together with what Regiments are referred to in that index, explained on this site:

http://www.revwar75.com/ob/m246.htm

You can then use the Compiled Service Records for each of the Campbells in each Regiment to find one listed as died in 1778. You can browse through them by regiment on ancestry.com, or use the index and searching features for the Compiled Service Records on www.footnote.com, which has free trial periods where you can view the compiled service records.