There are two stages to attacking a Zone Menace.
First step, send your Hero Squad to Challenge and weaken the Menace.
The Zone Challenge will last for 90 seconds, consuming a Challenge Attempt in the process no matter if you win or lose.
Damage dealt will decrease the Menace’s Total HP. When the Menace’s Total HP hits zero you can send your troops to attack the Menace’s supporting legions. Each March will reduce the Troop Power of the Zone Menace.
When the supporting legions are eradicated and the Power is zero, the Zone Menace will be fully defeated.
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Game Guide for State of Survival: Survive the Zombie Apocalypse