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