Here is the full list of all 15 Mushroom Wars achievements.
Win a Skirmish game
Complete Campaign
Achieve level 5 morale
Capture 300 enemy buildings
Encounter aliens in Campaign
Encounter forest warriors in Campaign
Complete Campaign on highest difficulty
Complete Campaign in under 60 minutes.
Earn each reward at least once
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
Achieve maximum attack level