Here is the full list of all 32 Factory Town achievements.
Complete Campaign Map 8
Create 1 Fire Ring
Create 1 Water Ring
Upgrade Base to level 10
Create 1 Magic Cloak
Complete Campaign Map 7
Craft 1 Omnistone
Create 1 Elixir
Create 1 Berry Cake
Complete Campaign Map 6
Complete Campaign Map 5
Complete Campaign Map 4
Complete Campaign Map 3
Create 1 Fish Stew
Complete Campaign Map 2
Create 1 Warm Coat
Craft 1 Fire Crystal
Create 1 Water Crystal
Create 1 Earth Crystal
Create 1 Air Crystal
Create 1 Mana Crystal
Create 1 Meat Stew
Create 1 Veggie Stew
Create 1 Crown
Create 1 Necklace
Create 1 Iron Plate
Earn 1 Blue Coin
Earn 1 Purple Coin
Complete Campaign Map 1
Complete any Research
Earn 1 Red Coin
Earn 1 Yellow Coin