The description for this is, I think, a bit confusing. You need to have 20 edicts active at the same time, it is NOT a cumulative total, so you can't just keep issuing the Tax Cut edict, for example.
Start a sandbox game in the Modern Times era, economic/political difficulties as very low and unlimited money so you can issue all the edicts straight away. Some will require certain buildings to be built before you can issue them, even so you should be able to issue 20 edicts from the available ones. Just don't worry about the impact they'll have as you can quit as soon as the achievement pops.