Here is the full list of all 12 Super Algebrawl achievements.
Rule the Fractal Grove
Rule the Epsilon Estuary
Rule the Binary Bay
Gather 10 stars
Gather 20 stars
Gather 30 stars
Have a mouse for each number from 1 to 9
Have 3 monsters in your army
Get a soldier with 100000+ hp
Get a worm with 1000+ hp
Finish a stage with at least 3+ permanent skills
Have 15+ soldiers in your army