This achievement is easily obtainable in the first mission of the campaign.
Do not choose to start a revolution when prompted/asked to do so (Approval 50%+) while maintaining your mandate from the Crown to rule Tropico for 100 months.
You'll start with 4 years (4y, lower left on the HUD).
From time to time a marker will appear near your palace. Select it with
and choose to fullfill whatever the crown is asking from you (i.e. build a sugar plantation or export x-amount of crops). As a reward always choose an extention on your mandate.
For me the achievement popped when I still had 4 years and 11 months left as a governor.
If you have any questions feel free to comment. If I can improve on this solution please let me know as well!