Here is the full list of all 16 Rover Wars achievements.
Win without taking base damage and without dying
Deploy a deathray that costs more than 100 resources
Deploy a deathray that costs more than 300 resources
Play every battle mode level once
Win a game by only building bombers
Win a game by only building rocketeers
Win a game by only building melee minions
Win a game where you boost for more than 2 minutes
Win a game in a 1v4
Damage more than 6 minions in 1 hit
Let 4 bots fight 4 bots
Destroy 50 units
Destroy 500 units
Destroy 5000 units
Use the Konami code to get more health
Finish the campaign