This is achieved in the challenge called "Number One Threat to America". It is an optional mission, located in the USA and unlocks early-mid campaign. The map is square, with a lake in the middle, and 25 giant bears in green armour are roaming or swimming around the area.
The bears are pretty tough but vulnerable to air units. They're not hidden, so sweep the whole map to ensure you've not missed any. Upon killing the last bear, the achievement will unlock.
Try not to completely obliterate the other enemies on the map or the mission may end prematurely. You may want to significantly weaken (but not destroy) the base before going after the bears.
If you fail, you can restart the mission from the world map.