Here is the full list of all 15 Mushroom Wars achievements.
Earn each reward at least once
Win a Skirmish game
Complete Campaign
Achieve maximum attack level
Achieve level 5 morale
Encounter aliens in Campaign
Capture 300 enemy buildings
Encounter forest warriors in Campaign
Complete Campaign on highest difficulty
Complete Campaign in under 60 minutes.
Earn all 9 rewards in a single Campaign level
Earn all rewards in all Campaign levels
Achieve victory on all Skirmish maps on highest difficulty
Upgrade your village to level 5
Capture an enemy building without having any of your own