Complex sentence: Despite this embarrassing defeat, Chalmers went on to have a successful military career, taking part in the Kentucky Campaign under General Braxton Bragg and as a brigade commander at the Battle of Stones River, where he was wounded at "Hell's Half-Acre".
Split into simpler sentences: Despite this embarrassing defeat, Chalmers was considered to have had a successful military career, taking part in the Kentucky Campaign under General Braxton Bragg. He was a brigade commander at the Battle of Stones River, where he was wounded at "Hell's Half-Acre".