Valkyria Revolution

basically what you need to do is capture an enemy territory during a skirmish that isn't story related.

complete the standard mission (marked with a pin) on a capturable area twice without skipping a spawn inbetween, the takeover mission will spawn immediately (which is called "reclaim Avalune" for example) right after your 2nd win in a row to take over the area that gives you this achievement

if you can not capture an area due to story reasons, you'll get the "encounter at" mission, which is basically the defense battle mission and will NOT give you this achievement

keep in mind that when you do a 2 part story mission, the board will still change inbetween the 2 missions while you're at the camp, so you might miss a spawn if you don't check with suspend mission. which brings you back at the HQ and allows you to do a different mission instead of the story mission

Like mentioned above you need to reclaim a territory that is not story related.

If you are unable to spawn any such missions like me, just start up one of those defend territory missions.

Run away from your base and afk. Let your base be captured by the enemy.

Quitting the game does not count even though you lose the mission. It needs to be captured by the enemy.

Try doing missions in that captured territory and eventually a reclaim lost territory mission will appear on that area.

Finish the mission and get the achievement.