1 - From the main menu, choose play
2 - Select tutorial
3 - There are 4 parts to the tutorial. You want to chose part 1/4 of the tutorial. This is the default part of the tutorial screen that loads automatically after you select tutorial.
4 - press A to either start or restart part 1 of 4 of the tutorial
5 - When the game loads, you now have to press A 3 times to get by the 1st three tutorial messages
6 - Now press LT and Y to bring up the almanac
7 - Using LB or RB scroll to the lists tab
8 - On the lists tab, select residents-origin
9 - On the right hand side of the page, you will see Tropico with a total of 60 residents
10 - Press right on the DPAD to cycle through the names of each one of the residents until you find Juanito. Juanito is his 1st name. His last name may vary. (thx Sax89)
11a - If Juanito is not listed, press the start button, and select restart. Then repeat steps 5 through 10 above
11b - If Juanito is listed, press the A button to select him.
12a - If he is a child, in my opinion it is faster to repeat steps 5 - 10, then to wait for him to grow up so that you can select the eliminate option
12b - If Juanito is an adult, using the dpad, select the eliminate option (it costs $500). It is the 4th icon from the left in the second row of icons beneath his name and it looks like a bullseye.
13 - Press A.
14 - You will be prompted "Are you sure you want to issue this order?"
15 - Press A
16 - The soldiers in the palace will now kill him and the achievement will pop.
Note - I have tried this method personally around 15 times. The name Juanito appeared 4 fo the 15 times. 1 of the 4 times Juanito was a child. The other 3 times he was an adult. Once you get the process down (steps 5 -10), it should take no longer than 15 minutes to find an adult Juanito and get the achievement.
Final note - Once you have selected to eliminate Juanito. Set the game speed to its fastest setting. It should only take upto a minute before he is killed and the achievement pops.
Hope this helps