I agree with MastaGus on using the Cursed Island campaign mission. What I will do is give a bit more detailed information on making it somewhat easier to get done.
As a major side note, save after every event you get. I ended up with roughly 15 different saves on this one game.
1st thing is to make sure you set all your avatar attributes to something to help increase farming (speed & production). On your initial start go and create 4 tobacco farms just above and to the right of the palace (you can see the darker green section and throw the 4 in a general circle putting each farm near the outside corners so they farm the middle green sections). This will get you a pretty good steady flow of cash to build up stuff to keep people happy enough while you go through the 25-40 years it will take for this cheevo. Make sure to connect the 4 farms to the main road leading to the palace so the teamsters can get the stuff to the dock quicker.
Next thing is to make an immigration office (making sure you have enough cash not to go into a nagative balance, make sure to have around 3-4k left after its built) and set it to open door as soon as possible. Just hire 1 foreign HS person for it initially. By this time you should have had your 1st event (I had mine in 1953) and possibly lost 1 or 2 things. Replace what you lost (if needed) and at the earliest chance (without going into negative cash flow) put an armory next to the palace and hire at least 2 foreign generals to defend since your approval ratings will be in the toilet.
At this point throw down another tobacco farm and possibly 1-2 more corn fields. I increased all farmers only wages to 7 to make sure they stayed filled and busy. By the 8th year (and my 2nd event - 1957) I was pulling around 15-30k average per freighter
Once your around 110-125 people close up tropico to foreigners and just work on building up the infrastructure.
Once your around 1960 you should be pulling in good amounts of money and now you will start putting down apartments, some small entertainment and at least 1 clinic & church (hire people for them or build a high school and train people to fill in the spots). Doing this will allow you to make sure people don't hate you too much and try and boot you out of office by rebellion or uprising.
I only suggest doing this initially since you will need to have a good flow of income to get to the 1975 or so needed (without a coup, rebellion, etc) to get the 10 events.
I'm not making a big deal about housing, entertainment or religion for the 1st 7-10 years since I didn't make a difference to me either time I went through the senario with the above method.
Once you hit around 1962 you should have had your 3rd event
(I had my 3rd at 1960 but it is completely random as I will explain below) and now the fun part starts. This is where you will get bored but this is the best and easiest method I have found.
Starting around 1964 make sure your generating a large positive cash flow and you have a good amount of the general buildings done and being used (apartments, high school, possibly a college, 2 clinics, at least 2 teamster offices, 2 restaurants, 1 church and possibly a cathedral) and an above average military/police presence since your not going to be doing much to mess with your city after this. Guard towers are handy as well to put near the farms you built since that is where the rebels will more then likely go to start trouble.
When your all set with this you will start running the 3 year saving/reload game. If you do not have your 4th event by the end of 1967 reload your saved game. You will have this main save done with at least 3 events and all your above stuff built so you don't need to mess with anything at all when you reload it. Keep doing this until your get an event. Once the event hits (no more then 3 years after this main save) replace any buildings and then save it again. I ended up getting events in 64, 66, 67, 70, 71, 74 & 76 to get the cheevo (it popped as soon at the 10th event started for me).
You may not need to do as much as I put above but it made things easier since I could let it run 3 years and not need to worry about doing anything except wait for the event.
Hope this helps and since the game is really random, things may be different for you but this worked the 2 times I did this.