This achievement turned out to be rather easy. When you start the game in 1776 you are at war with GB and soon after a couple of nations will join in the war against you. Hesse, some Indian nations and the Iroquois Indians. Except for the latter none of these will actually send troops to attack you. To get at least a white peace you will need around 36% war score.
GB has a bigger fleet then yours so best to keep your fleet in harbor. GB wil then send waves of 29k armies which will land in your most northereast province. As amphibious attacks get a -2 penalty all you need to do is put your main army with it´s best general to intercept and exterminate each invading army. After three susch landings GB will accept a white peace and might even offer some territory in North America.
The Iroquois are best taken out before they take your land by claiming their capital.
Optional is to have a token army conquer the british provinces in North America which offer a tiny war score bonus.