For this achievement it's a good idea to build up a decent island, so play a sandbox game and make it as easy as possible, you want to do things like, set the terrain to flat, random events to none, vegetation to high etc.
By the time you're going for this achievement the chances are you'll have played a few games of this and have an idea on how to set up a decent island so I won't go into loads of detail but here's some basics.
Create a few tobacco farms, when you can afford it build a school to educate your workers, build a cigar factory and from there keep expanding, keep growing your economy, keep your population happy so they don't throw you out.
Now, this may all sound long winded for an achievement which says; "in one game" but just disregard that, even once the the timer has run out you can choose to "keep playing" and keep working toward this achievement.
Before you go for this achievement you might want to make a separate game save so that once you've got this achievement you can go back and work on another without having to keep setting your island up! (Be aware of the saving glitch though, see here; Tropic 3 Crash
Now, in case you haven't done so already you need to establish a secret police for this achievement, to do so you need to build a police station and for this method it's a good idea to build one in amongst a whole bunch of housing, once your police station is built, activate the "Secret Police" edict and then when it asks you to place a HQ for them pick the police station you just built.
Now go around and keep selecting citizens and you'll be able to arrange for them to have an accident, without emptying your treasury do this to as many citizens as your comfortably can afford, the more the better. Keep doing this until you get the achievement, make as many saves as you want, just keep using that second save you made earlier and keep an eye on your population count, you don't wanna spend an hour on this achievement just to go and corrupt your save!
It might take what feels like forever but you will eventually get the achievement!
Right, just in case anyone was wondering why you should use this set up I'm going to explain a bit below.Why should I build up a stable economy and keep my population happy?;You want a strong economy so that once you go for this achievement you can just sit back and keep letting the money roll in, I was getting 120k+ per freighter export, this is also why you want a happy population, it's no good getting everything set up just to get overthrown at the last stage, you want it so you can just sit back and do nothing but focus on this achievement!Why should the secret police be amongst a bunch of housing?;Because accidents can only happen when the person is at home, having your secret police right in among a bunch of homes will make the chances of them being able to get in arrange the accident while they're at home that little bit higher!
Right, that's all I have for you! Good luck going for this, just be patient, it will unlock eventually!