All you need is three rivals and three diplomats build spy network up to maximum 100. so It's a good idea to have at least 4 diplomats before attempting this. so you can still do other things during the 5+ years it will take you to reach 100.
You can get an extra diplomats with some idea's or by being the curia controller.
there is about 2% chance of discovery each month and the build speed around 1.5/month.
so a minimum of 5,5 years if your not discovered. when discovered either quit and reload the backup save or simply wait 2 months and put the diplomat back into business and accept that you might have lost a year worth of spy networking. eventually all three will reach 100 at the same time. and this achievement will be yours!
There is of course way to improve these numbers such as advisers, ideas etc but they aren't that bad and you might want to focus on other long time goals.