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The description of the achievement can be confusing.

It should read 'any' instead of 'all'.

You get the achievement as soon as you capture 3 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.