Checkpoints are on the roads throughout Yara and you need to kill all the enemies and destroy the billboard in order capture the checkpoint.
The quick method I did was hop into a tank (If you need one use the EMP blast and hijack one. Bring it back to a vehicle call station so you can get one whenever you want) once in the tank just drive a lap around the main road and capture every checkpoint as you come across them. It took me around 45 minutes to get 10 with no trouble. Occasionally you'll have to hop out your tank and repair it.
You can accomplish two other achievements while doing this:
As you are blowing up the checkpoints you will gain heat (the 2 bars next to the map in the bottom left of screen) and once you gain heat you'll attract the elite soldiers also. Just kill 10 soldiers while having heat and 10 elite soldiers as they show up which will be easy being you are in a tank.