First off, read the achievement. Some people assume that you need to win the civil war as the Confederates to unlock the achievement, when it only says "start a new civil war." With that out of the way, wait until the 1936 election and put Alf Landon (Republicans) in power, then immediately go for "Reestablish The Gold Standard," followed as soon as possible by "America First" and "Ally With The Silver Shirts." As soon as that third focus completes, you'll start a timer with multiple events. No matter what you do from this point on, you'll eventually see New England secede (followed by other states) and the Constitutionalists will launch a civil war. The achievement should trigger as soon as the war starts.