The description of the achievement can be confusing.
It should read 'any' instead of 'all'.
You get the achievement as soon as you capture 10 tiles on any continent.
You should make that correction on all the achievements of this type.
Capture is different from bought.
You do this by using a hero from an academy and fight to conquer the tile.
In practice, you will get this by normal gameplay on the first continent.