A "msn.com" search expands on Goggle, and gives us a list of engagements and also a roster of the company.
Interestingly, there was also a Missouri Infantry unit by the same name.
A unit by this name, Breckenridge Guards, is not included in the Compied Service Records of Confederate Soldiers Who Served in Organizations from the State of Mississippi. At least not in my Military Service Records Catalog. Perhaps they also carried another unit designation.