Here is the full list of all 12 Forest Plague achievements.
Get through 1 wave
Get through 10 waves in a row
Get through 30 waves in a row
Try all the available weapon types
Defeat a boss for the first time
Defeat 25 bosses
Kill 1000 enemies
Improve your health to the 10 level
Improve regeneration to the 10 level
Improve armor to the 10 level
Kill one common creature of each type
Reset your progress and start again with improved characteristics