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