Here is the full list of all 20 Save the Planet achievements.
Pass 3 wave
Pass 7 wave
Pass 15 wave
Pass 25 wave
Pass 40 wave
Complete 1 wave in difficult mode
Complete 3 wave in difficult mode
Complete 5 wave in difficult mode
Complete 6 wave in difficult mode
Complete 7 wave in difficult mode
Destroy 5 aliens
Destroy 15 aliens
Destroy 30 alien
Destroy 50 alien
Destroy 100 alien
Accumulate 100 points
Accumulate 250 points
Accumulate 500 points
Accumulate 1000 points
Accumulate 3000 points