Tropico 5 - Penultimate Edition

This solution was originally posted for the 360 version, but I finally got around to using it for the XBox One version, and it worked just fine. A couple edits have been made from that solution:

In order to achieve this, I started a new, Sandbox campaign, with unlimited funds, 'Modern Times' technology-age, 50 starting people, and every other setting on 'very low' or 'none' EXCEPT political difficulty, which I set to 'very high.' -- I chose "Puerto Coco," though I doubt choice of island matters, at all.

1) The first thing I did was quick-build a 'Military Fort,' (with colonial soldiers) -- DO NOT upgrade the fort, as this will be the source of the coup, and you'll want your palace death squad troops to defeat them, easily.

Here were my next steps:

2) Lower pay in all buildings to level 1 pay, except the palace, which I lowered to level 2 pay.

3) I happened to have a 'Foreman' in my dynasty, so put him in charge of the Military Fort (to lower job satisfaction more), and put a 'General' from my dynasty in charge of the Palace. Additionally, I upgraded my Palace troops to 'Personal Death Squad.' If you don't have similar Manager options in your dynasty, you might still hire managers from your population with desirable effects.

4) I fired everyone in the Construction Office, and locked-out that office from re-hiring anyone. Optionally, you may also enable various edicts that will increase unrest, such as a Tobacco Ban, Prohibition, Same-Sex Marriage, etc. (thanks for this suggestion, ViZ Kenthelux & zoidberg1339 )

5) Once the Military Fort had a full contingent of troops, I looked at each individual troop's Approval Rating of me (click on fort, cn_RB once to troop page, cn_right to a specific troop, and click cn_Y to look at that soldier's approval of you), and assassinated any soldier with an Approval Rating above 25 -- this helps to make the Fort's soldiers more disgruntled.

6) I then put the game on high-speed, to await some sort of unrest to happen, and to let my soldiers' loyalty % decrease (check this with cn_LT + cn_X, and scroll down with cn_RB to the 'Political' tab). If any peaceful protests happen during this time, "Send in the Army" to quash the protest. Perhaps unnecessary to mention, but should you get a notice regarding elections, choose "No need for elections," as clearly, your people love you, and we don't need elections muddying our attempt.

7) Eventually, I lowered the Palace pay rate down to the lowest level, as well. By the time soldier loyalty % hit 15-17%, you should have "High," or even "Very High" unrest levels. Continue on, as it's just a waiting game, at this point.

8) When the coup happens, SAVE YOUR GAME immediately. Since the Military Fort has ONLY soldiers who have VERY low opinions of you, the coup will have happened here, so you'll only have a squad of Colonial Soldiers to deal with, using your 'Personal Death Squad' palace troops.

Once your palace troops have dealt with the fort soldiers, the achievement will pop. If, by some miracle, the colonial soldiers (with 41 attack rating) beat your palace troops (with 62 attack rating), then re-load your save and let the fight happen, again -- but, this shouldn't be a problem.

Build a lot of army bases and barracks and try appointing generals in the barracks and tactitians in the bases. Having at least 5 bases and 5 barracks. A few forts with cheapskate managers doesnt hurt either. What this does is allow your strongest army (bases with tanks) to be more immune to coup activity via tactitians and your weaker units to be the most prone to going coup de tar.

Reasonably straight forward in a sandbox game where youll have the resources and time to do it.