Here is the full list of all 17 Fungoids - there are Steam version achievements.
Complete 1 level in classic mode
Complete 2 levels in classic mode
Complete 3 levels in classic mode
Complete 4 levels in classic mode
Complete 5 levels in classic mode
Complete 1 level in alpha mode
Complete 2 levels in alpha mode
Complete 3 levels in alpha mode
Complete 4 levels in alpha mode
Complete 5 levels in alpha mode
Destroy your first Fungoid
Run out of bombs
Run out of fuel
Destroy your first Mushoid Man.
Survive 1 minute
Survive 5 minutes
Survive 10 minutes